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All Theses and Dissertations
2010-08-09
Beta Galactosidose Activity of Commercial Lactase
Samples in Raw and Pasteurized Milk at
Refrigerated Temperatures
Trenton W. Horner
Brigham Young University - Provo
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Horner, Trenton W., "Beta Galactosidose Activity of Commercial Lactase Samples in Raw and Pasteurized Milk at Refrigerated
Temperatures" (2010). All Theses and Dissertations. Paper 2590.
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Beta-Galactosidase Activity of Commercial Lactase
Samples in Raw and Pasteurized Milk
at Refrigerated Temperatures
Trenton W. Horner
A thesis submitted to the faculty of
Brigham Young University
in partial fulfillment of the requirements for the degree of
Master of Science
Lynn V. Ogden, Chair
Michael L. Dunn
Frost M. Steele
Dennis L. Eggett
Department of Nutrition, Dietetics, and Food Science
Brigham Young University
December 2010
Copyright © 2010 Trenton W. Horner
All Rights Reserved
ABSTRACT
Beta-Galactosidase Activity of Commercial Lactase
Samples in Raw and Pasteurized Milk
at Refrigerated Temperatures
Trenton W. Horner
Department of Nutrition, Dietetics, and Food Science
Master of Science
Many consumers are unable to enjoy the benefits of milk, due to lactose-intolerance.
Lactose-free milk is available, but at about 2 times the cost of regular milk or greater, it may be
difficult for consumers to afford. The high cost of lactose-free milk is in part due to the added
cost of the lactose hydrolysis process. Hydrolysis at refrigerated temperatures, possibly in the
bulk tank or package, could increase the flexibility of the process, and potentially reduce the
cost.
A rapid β-galactosidase assay was used to determine the relative activity of commercially
available lactase samples at different temperatures. Four enzymes exhibited low-temperature
activity and were added to refrigerated raw and pasteurized milk at various concentrations and
allowed to react for various lengths of time. The degree of lactose hydrolysis by each of the
enzymes as a function of time and enzyme concentration was determined by HPLC.
The two most active enzymes, as determined by the β-galactosidase assay, hydrolyzed
over 98% of the lactose in 24 hours at 2⁰C using the supplier recommended dosage. The other
two enzymes hydrolyzed over 95% of the lactose in 24 hours at two times the supplier
recommended dosage at 2⁰C. Results were consistent in all milk types tested. The results show
that it is feasible to hydrolyze lactose during refrigerated storage of milk using currently
available enzymes.
Keywords: lactose-free milk, lactase, β-galactosidase, lactose intolerance
ii
ACKNOWLEDGEMENTS
I would like to thank Dr. Lynn Ogden for his expertise and support on this project
including his feedback for this manuscript. Thanks to my graduate committee for their
contributions to this project. Thanks to Dr. Jiping Zou for his help in analyzing the lactose
content of many milk samples. Thanks to Dr. Joel Griffitts for his expertise and advice regarding
the β-galactosidase assay. Thanks to Scott Lewis for his help on the project. I would especially
like to thank my family for their love and support throughout my educational experience.
iii
CONTENTS
INTRODUCTION ............................................................................................................................................. 1
MATERIALS .................................................................................................................................................... 4
Enzymes .................................................................................................................................................... 4
Milk Samples ............................................................................................................................................. 4
METHODS ...................................................................................................................................................... 5
β-galactosidase assay ................................................................................................................................ 5
Hydrolysis in chilled milk ........................................................................................................................... 6
High Performance Liquid Chromatography Analysis ................................................................................ 7
Data Analysis ............................................................................................................................................. 8
RESULTS AND DISCUSSION............................................................................................................................ 8
Relative activity of commercial enzymes .................................................................................................. 8
Lactase activity in chilled milk ................................................................................................................... 9
Effect of different milk types .................................................................................................................. 11
Applicability to the industry .................................................................................................................... 11
Cost Analysis ........................................................................................................................................... 12
CONCLUSIONS ............................................................................................................................................. 13
REFERENCES ................................................................................................................................................ 14
APPENDICES ................................................................................................................................................ 22
APPENDIX A ................................................................................................................................................. 23
APPROVED PROSPECTUS ............................................................................................................................ 23
Proposed Title: ........................................................................................................................................ 24
Statement of the problem ...................................................................................................................... 24
Method to be followed ........................................................................................................................... 25
Justification of the problem .................................................................................................................... 25
Delimitations of the problem .................................................................................................................. 26
APPENDIX B ................................................................................................................................................. 27
TESTING RELATIVE ACTIVITY OF THE ENZYMES: THE BETA-GALACTOSIDASE ASSAY ................................ 27
Appendix B-1: Solutions ......................................................................................................................... 30
Appendix B-2: Spectrophotometer ........................................................................................................ 31
Appendix B-3: Explanation of the how the β-Galactosidase assay works ............................................. 32
iv
APPENDIX C ................................................................................................................................................. 33
HPLC ANALYSIS OF LACTOSE HYDROLYSIS .................................................................................................. 33
Appendix C-1: Solutions ......................................................................................................................... 36
Appendix C-2: Results of HPLC Analysis ................................................................................................. 37
APPENDIX D ................................................................................................................................................. 44
STATISTICAL ANALYSIS OF HPLC DATA ........................................................................................................ 44
v
INTRODUCTION
Milk is a nutrient-dense food and an important part of a healthy diet. Along with highquality protein, milk contains many vitamins and minerals, such as riboflavin and calcium (Choi,
2007). Milk is fortified with vitamin D and is one of the few commonly consumed food products
containing this vitamin (Mannion, 2006). Unfortunately, many consumers are unable to enjoy
the benefits of milk due to lactose-intolerance (Choi, 2007; Somkuti, 1997; Husain, 2010).
Lactose intolerance is caused by a deficiency of β-galactosidase (lactase) in the digestive
tract (Panesar, 2007). Lactose is a milk disaccharide composed of glucose and galactose bonded
with a β-1→4 linkage. Normally, lactose in milk is hydrolyzed by β-galactosidase located in the
mucosal cells of the small intestine. β-galactosidase hydrolyzes lactose into its respective
monosaccharides which are easily absorbed and metabolized (Gropper, 2005).
When lactose intolerant individuals consume milk, the undigested lactose passes into the
colon and increases the osmolarity of the digested food. This inhibits the absorption of water by
the colon and can cause diarrhea. Also, bacteria in the colon are able to digest the lactose, which
causes increased acidity and the production of gas and toxins (Choi, 2007). These unpleasant
symptoms may inhibit the consumption of milk by lactose-intolerant consumers (Messia, 2007).
The amount of lactose needed to cause symptoms can vary widely from person to person.
Some lactose-intolerant individuals are unable to consume any lactose without experiencing the
symptoms of lactose-intolerance while others are able to consume some milk without
experiencing symptoms or with only mild symptoms (Choi, 2007). Cultured dairy products such
as yogurt and cheese often have significantly lower levels of lactose and many lactose-intolerant
individuals are able to eat them without symptoms (Sieber, 1997).
option consumers have available (Somkuti, 1997).
1
Lactose-free milk is another
Lactose-free milk is commercially prepared by allowing β-galactosidase enzymes (E.C.
3.2.1.23) to hydrolyze the lactose present, prior to packaging. This allows consumers to gain the
valuable nutrients and protein available in milk without unpleasant symptoms.
While enzyme-altered lactose-free milk is available, it is expensive, and many consumers
are unwilling or unable to pay for the extra cost. Lopez and Lopez (2009) report high-income
families are the main consumers of lactose-free milk. As household income rises, the purchase
and usage of lactose-free milk products also rises (Mintel, 2010). The higher cost of lactose-free
milk is due in part to the cost of the hydrolysis process used by manufacturers. It is hypothesized
that if enzymes were sufficiently active at the temperature of chilled milk, the hydrolysis reaction
could be carried out under refrigeration during transport or storage in trucks, tanks, or final
packaging. By doing this, the cost to manufacture lactose-free milk might be reduced.
The market for lactose-free milk has been growing for years. Jelen (2003) predicted
about a 20% per year increase in the market. This expected increase was due in part to the
increased awareness of lactose intolerance. The market for lactose-free milk is estimated at 3050 million consumers in the U.S. alone (Adhikari, 2009). Lactose intolerance is more common
in some ethnic groups than others (FDA, 2009). Among African-Americans and Native
Americans it is about 75%; among Asian populations it is about 90% (FDA, 2009). With such a
large potential market for the product, reducing the cost of lactose-free milk could significantly
increase its consumption.
Reduction of lactose in milk has been explored using many different methods.
Traditionally, soluble β-galactosidase enzymes are added to milk. Panesar and others (2007)
explored the use of immobilized enzymes. Novalin and others (2005) describe using an
innovative hollow-fiber ultra-filtration process with immobilized enzymes. Another study
2
described using ultra-filtration and concentration by evaporation, then adding the enzymes to the
concentrated permeate and later adding the hydrolysate back to the retentate (Chen and others,
2002).
Lactose-free milk that has been treated with β-galactosidase is sweeter than regular milk
due to glucose and galactose being sweeter than lactose, combining to be about 70% of the
sweetness of sucrose as compared to lactose, which is only 20% the sweetness of sucrose
(Novalin, 2005). This sweetness may be advantageous for certain products such as ice cream but
alters the flavor of milk used for drinking. Choi and others (2007) have shown that the resulting
sweetness can be removed by utilizing nanofiltration and reconstituting the milk. Harju (1989)
describes a chromatographic process to separate the lactose from the protein and other
components of milk, completely removing lactose without the use of enzymes and without any
residual sweetness. However, none of these or other methods reported in the literature have the
potential to significantly reduce the cost of producing lactose-free milk compared to traditional
methods.
β-galactosidase enzymes are commonly harvested from microorganisms such as fungus,
yeast, and bacteria; for example, Kluyveromyces lactis is a commonly used yeast for producing
β-galactosidase in the industry (Dabhole, 1998). Enzymes sourced from yeast or bacteria are
well suited for the hydrolysis of lactose in milk, often displaying an activity optimum near the
pH of milk (Chen, 2009). A fungal β-galactosidase is typically used in acidic dairy applications,
such as sour cream (Chen, 2009).
A number of bacterial β-galactosidase enzymes, having optimum hydrolytic activity at
temperatures lower than is normal for lactase enzymes, have been isolated (Fernandes, 2002;
Coker, 2006). Many lactases have optimum temperatures above 30⁰C, whereas cold-active
3
lactases can have temperature optimums of 15⁰C or below (Coker, 2006). Bacteria adapted to
colder climates can be found in soil and isolated for β-galactosidase production (Coker, 2003).
Cold-active β-galactosidase has also been isolated from psychrophilic yeasts, which may be
suitable for food use (Husain, 2010). Thus, there is a potential for developing lactase enzymes
with significantly increased activity at refrigerated temperatures.
The objective of this research was to determine if currently available lactase enzymes are
active enough in chilled milk to enable the hydrolysis process to be carried out during
refrigerated storage.
MATERIALS
Enzymes
Five commercially available food-grade β-galactosidase enzymes were obtained from
four separate distributors. The enzymes examined in the initial screening included the following:
GODO-YNL2 yeast neutral lactase (DYL) (Danisco A/S, Copenhagen, Denmark), Validase®
yeast lactase (VYL) and Validase® fungal lactase concentrate (VFL) (Valley Research, South
Bend, IN, USA), Enzeco® Lactase NL (EYL) (Enzyme Development Corporation, New York,
NY, USA), and Lactozym® lactase (LYL) (Sigma-Aldrich, St. Louis, MO, USA).
The DYL, VYL, and LYL enzymes were derived from Kluyveromyces lactis and the
EYL enzyme was derived from a Kluyveromyces sp. VFL was derived from Aspergillus oryzae.
The supplier recommended dosages for the enzymes are as follows: 0.1% w/v for the DYL, VFL,
EYL, and LYL enzymes and 0.08% w/v for the VYL enzyme.
Milk Samples
The rate of lactose hydrolysis by the enzymes in chilled, raw, whole milk; pasteurized
whole milk; and pasteurized skim milk was determined at refrigerated temperature. The raw
4
milk was obtained from the Brigham Young University creamery and originated at the Elberta
Valley Agricultural Dairy Farm (Elberta, Utah, USA). The raw milk had an average of 3.51%
milkfat, 3.11% protein, and 5.94% other solids. Raw milk data was determined by using a
Lacticheck milk analyzer (Page & Pedersen International, Ltd., Hopkinton, Massachusetts,
USA).
The pasteurized/homogenized skim milk and whole milk were obtained from the local
market. The skim milk had less than 0.5% milkfat and whole milk had approximately 3.25%
milkfat. Each type of milk was tested using each time/concentration combination (described
below), which required the preparation of 65 samples for HPLC analysis for each trial run (195
samples in total for the three types of milk).
METHODS
β-galactosidase assay
The relative activities of the enzymes were analyzed using a modified version of the βgalactosidase assay of Miller (1972). This assay involves hydrolysis of O-nitrophenyl-β, Dgalactopyranoside (ONPG) to O-nitrophenol (ONP), which produces a yellow color measurable
via spectrophotometer (Switzer and Garrity, 1999). The assay takes little time to perform and is
helpful for comparing the relative activity of β-galactosidase enzymes.
To obtain a temperature-activity profile and compare relative activity, assays were carried
out at 4⁰C, 10⁰C, 20⁰C, and ambient (~23⁰C) temperature. The non-ambient temperature trials
were performed using a Percival I-36NL controlled atmosphere chamber (Percival Scientific,
Inc., Perry, Iowa, U.S.A.). As the assay was originally intended for analyzing β-galactosidase
production by bacteria, the assay reagents reacted very quickly when exposed to purified
enzyme. To accommodate the higher activity of the commercial enzymes, the samples were
diluted 10-5 (ambient temperature and 20⁰C) and 10-4 (4⁰C, 10⁰C) with basal buffer to allow a
5
reaction time similar to the bacterial assay. Approximately 450 µl of basal buffer was combined
with 50 µl of each enzyme in microfuge tubes (1.5 ml). Approximately 600 µl of assay buffer
was then added to each sample and the start time of the reaction was recorded.
Color development was measured at 420 nm using a Milton Roy Spectronic 1001
spectrophotometer (Milton Roy Instrument Group, Rochester, New York, U.S.A.). Samples
were allowed to react until a faint, but stable yellow color developed (between 0.1 and 1.0 on the
spectrophotometer). The reaction required 20-40 minutes on average, after which a stop buffer
(sodium carbonate) was added to halt the reaction.
The data were used to calculate the change in optical density at 420nm (ΔOD420) per
minute (T) per volume (V) of enzyme sample according to the following equation, adapted from
Miller (1972): ΔOD420 per minute per volume = [1000*OD420] / [T(min)* V(ml)]. The
ΔOD420 per minute per mass (ng) of protein of each enzyme was then calculated by adjusting
for protein content in each stock enzyme solution using the following equation: ΔOD420 per
minute per mass (ng) = [1000*OD420]/[T(min)*mass of protein(ng)] where protein mass is
calculated from the following: Volume(ml)*(mg/ml of protein in the enzyme solution) *
(dilution factor) * 106 ng/mg where volume is the amount of enzyme solution used in the assay
(0.050 ml), dilution factor being the dilution used for each trial (either 10-4 or 10-5). The mg/ml
protein of each enzyme preparation was obtained using the Dumas method (Nielsen, 2003).
Based on the activity comparisons of the enzymes, 4 out of 5 of the enzymes were
sufficiently active at refrigerated temperatures to be evaluated further in chilled milk. The VFL
enzyme demonstrated low activity under refrigeration and was not evaluated in milk.
Hydrolysis in chilled milk
Duplicate experiments were conducted for each type of milk using two different lots.
Lactose content was determined after 12, 24, 48, and 72 hours of reaction time. Where x is the
6
supplier’s recommended level of enzyme concentration, 0.25x, 0.5x, 0.75x, and 1x were used for
DYL and VYL and 0.5x, 1x, 1.5x, and 2x were used for EYL and LYL. Greater activity was
observed in DYL and VYL compared to EYL and LYL; hence, the higher concentrations for the
latter two enzymes.
The selected milk was put into 16 flasks (100 ml each). Four flasks were used for each
enzyme to allow all four concentrations to be tested. Once enzymes were added to the flasks and
swirled, the samples were stored in a walk-in refrigerator (2⁰C). Aliquots of 30 ml were taken
out at each time point and transferred to 50 ml plastic test tubes with screw-on caps, heated to
180⁰F, and held for 15 seconds to ensure inactivation of the enzymes to stop the hydrolysis
reaction. Lactose content was determined by HPLC.
High Performance Liquid Chromatography Analysis
The HPLC method of Wehr and Frank (2004) was used to determine percent lactose
hydrolysis based on disappearance of lactose. Milk or enzyme-treated samples (10 grams ±
0.0030) were weighed into 100 ml volumetric flasks using an analytical balance. Sulfuric acid (1
ml of 0.9N) was added using a mechanical pipette. The mixture was swirled to precipitate
proteins. Approximately 50 ml of de-ionized distilled water was added to the milk-acid mixture
and swirled again. Samples were then brought to volume (100 ml) with de-ionized distilled
water. Each flask was sealed and shaken vigorously for 20 seconds.
Samples were allowed to stand for at least 5 minutes, followed by filtering through 0.45
µm polytetrafluoroethylene (PTFE) syringe filters (Nalge Nunc International, Rochester, New
York, U.S.A.). Approximately 1 ml of each filtered sample was placed in auto-sampler vials and
sealed in preparation for HPLC analysis. Lactose analyses were conducted using an Agilent
Model 1100 HPLC (Agilent Technologies, Palo Alto, California, U.S.A.) equipped with a
7
Zorbax 70 A carbohydrate column, 5µm, 4.6x250mm (Agilent Technologies, Palo Alto,
California, U.S.A.). For comparison purposes, reference samples made from untreated milk
were analyzed in the same manner for each run.
HPLC separation conditions were as follows: gradient mobile phase of 75% acetonitrile,
25% water; 30⁰C; 1ml/min flow rate; 20 µl injection volume; refractive index detector. Data
was quantified using external calibration based on a standard curve.
Data Analysis
Data were analyzed using Statistical Analysis System software version 9.2 (SAS
Institute, Cary, NC). A mixed model analysis of variance procedure was used. The dependent
variable of the model tested for difference from 95% lactose hydrolysis (i.e. difference from
95%) with p<0.05. Analyses were also run at 98% and 99% lactose hydrolysis (difference from
98% or 99%). The independent variables included time, enzyme concentration, and the
time*concentration interaction. The statistical analysis is found in appendix D.
RESULTS AND DISCUSSION
Relative activity of commercial enzymes
In initial activity comparison tests in buffer (β-galactosidase assay), DYL and VYL
showed steep increases with rising temperatures, while EYL, LYL, and VFL were less affected
by the temperature range tested (see figure 1). Of the five enzymes evaluated at manufacturers’
recommended levels, DYL and VYL showed greater activity than EYL, LYL, and VFL (see
figure 1). This may be due to the higher protein concentration of DYL and VYL compared to
the other enzyme samples. VFL, specified for use in acidic dairy products, had very little
enzyme activity compared to the other four enzymes due its pH optimum (4.0 to 5.0) not being
within the range of the pH of milk (6.6 to 6.8) (Validase Fungal Lactase Concentrate
8
Specification, Valley Research, South Bend Indiana, USA). VFL was not included in further
experimentation.
Lactase enzymes produced from Kluyveromyces lactis commonly have a temperature
optimum above room temperature. Schneider (1990) found that lactase derived from this
microorganism had an 85% to 95% increase in activity at 38⁰C compared to the activity between
4⁰C to 5⁰C. DYL and VYL showed about a fourfold increase in activity at ambient (~23⁰C)
compared to the activity at 4⁰C. EYL and LYL showed much more modest increases.
When the results of the β-galactosidase assay were adjusted for protein content of the
enzyme samples (activity per mass (ng) of protein), the activities of the enzyme preparations
were similar to the activities of the enzymes when measured per volume, except LYL (see figure
1). At refrigerated temperatures, LYL had the highest activity per unit of protein, yet it
performed more poorly than the other enzymes during the assay. This is likely due to the LYL
having the lowest concentration of protein among the enzyme preparations tested.
Lactase activity in chilled milk
To determine lactose hydrolysis in milk for each enzyme, lactose content of pre-treatment
milk samples in each trial was compared to the lactose content after treatment. The galactose
and glucose peaks eluted at the same retention time during analysis and were inseparable without
a specialized column; this was consistent with the results of Sharma and others (2009). Thus,
percent hydrolysis was determined by disappearance of lactose.
The HPLC lactose peak area of each treated milk sample was divided by the area of the
respective un-treated milk sample to obtain a percentage of lactose remaining. That percentage
was then subtracted from 1 in order to determine percent hydrolysis.
9
Percent hydrolysis of lactose in refrigerated milk varied, depending on the enzyme
source, enzyme concentration, and reaction time. Performance of the enzymes correlated well
with the results of the β-galactosidase assay; the enzymes showing greatest activity in the βgalactosidase assay also hydrolyzed the most lactose in milk.
Percent hydrolysis for each of the four enzymes over time at a series of concentrations is
reported in table 1. Statistics for these values are reported in table 2. In pasteurized whole milk,
DYL hydrolyzed, on average, 99% of the lactose present in 24 hours at the supplier’s
recommended dosage. VYL showed an average of 98% hydrolysis in 24 hours at the supplier’s
recommended dosage. EYL and LYL were able to hydrolyze 95% of the lactose on average in
24 hours, when added at 2 times the recommended dosage.
Lactose hydrolysis can be achieved with less enzyme if the reaction is allowed to proceed
for a longer time. DYL achieved 95% average lactose hydrolysis in 72 hours while using onefourth the recommended dosage in pasteurized whole milk and 99% hydrolysis under the same
conditions using one-half the recommended dosage. VYL achieved 99% hydrolysis in 72 hours
using one-half dosage. EYL and LYL both accomplished approximately 99% hydrolysis on
average in 72 hours by using the recommended dosage.
Statistics shown in table 2 indicate the target levels of hydrolysis were achieved under the
stated conditions. Actual hydrolysis levels were not different than specified target levels as
indicated by the p-values. Since the intent of the process was to achieve at least the target level
of hydrolysis, p-values greater than 0.05 are indicative of the target hydrolysis levels being met
under the conditions indicated.
The results show the four commercially available enzymes are capable of hydrolyzing
95% or more of the lactose in milk within 24 hours using the recommended dosage (DYL and
10
VYL) or double the recommended dosage (EYL and LYL). All four enzymes can also
hydrolyze at least 99% of the lactose in 72 hours using half the amount of enzyme used in the 24
hours assays. Hydrolyzing lactose during refrigerated storage will allow greater processing
flexibility and potentially reduce the costs of producing lactose-free milk.
Effect of different milk types
The hydrolysis rate was not affected by fat content or processing. Hydrolysis in raw
whole milk, pasteurized skim milk, and pasteurized whole milk all proceeded at approximately
the same rate. For illustrative purposes, figure 2 shows the similarity of hydrolysis in different
milk substrates for LYL. All enzymes tested behaved similarly. The higher fat content of whole
milk did not impede enzyme performance. Enzyme concentration per volume was the same in
every milk type, even though the lactose content of whole milk is somewhat lower than skim
milk, due to the higher fat content. Despite the slight difference in lactose concentration between
skim and whole milk, the observed hydrolysis rates were similar across all three milk types.
Applicability to the industry
Lactose hydrolysis during refrigerated storage could be applied several different ways to
produce lactose-free milk. Adding the enzyme after pasteurization and homogenization and
bottling or packaging the milk without further processing is one possibility. By the time the
consumer would purchase the milk, the lactose would be sufficiently hydrolyzed. The enzymes
would have to be sterile filtered before adding to milk post-pasteurization (personal
communication, Cody Huft, Utah Department of Agriculture).
Another possibility would be to add the enzyme to raw milk before the milk is processed
at the plant. The enzyme could be added in the farm bulk tanks or in the tanker trucks used for
transport, allowing sufficient time for the lactose to be hydrolyzed before pasteurization and
homogenization. Such a process would require the farms and/or trucks to have dedicated tanks
11
for the purpose of lactose-free milk production. The enzyme could also be added to the holding
tanks at the plant, and hydrolysis could be accomplished while the milk is waiting to be
processed.
The possibility of Maillard browning may be of concern when hydrolyzing the lactose
before pasteurization; however, this does not appear to be a problem with lactose-free milk
products currently on the market. Maillard browning occurs when reducing sugars are heated in
the presence of protein (Fennema, 2008). The amount of reducing carbohydrate groups is
doubled once lactose is hydrolyzed into glucose and galactose (Messia, 2007). Dattatreya and
others (2010) found that once glucose and galactose have accumulated in sweet whey protein,
the whey may be predisposed brown more readily. This may also be true of milk. Addition of
sterile β-galactosidase post-pasteurization would avoid this problem (Messia, 2007).
The possibility of browning may also be avoided by using additional methods of
processing, such as the nanofiltration method utilized by Choi and others (2007) to remove the
glucose and galactose prior to heating. However, Messia (2007) found lactose-free milk which is
ultra-pasteurized after hydrolysis and stored at refrigerated temperatures to be acceptable. This
is in agreement with our own assessment of lactose-free milks from the local market.
Cost Analysis
Enzyme cost for each of the four enzymes, as determined at the time of this study, is
shown in table 3. The cost of the enzymes correlated well with the activity of each enzyme. As
the cost increased, the activity also increased. DYL, which hydrolyzed lactose the most
effectively at refrigerated temperatures, was the most expensive of the four enzymes with a
minimum volume pricing of $110 per kilogram. VYL, being the next most active enzyme, cost
$100 per kg. EYL cost $55 per kg and LYL cost $63 per kg. It is interesting to note that EYL
12
seems to be priced about the same as DYL on an activity basis, as EYL required twice as much
volume of the liquid preparation but only costs half as much as DYL.
By using a smaller dose and a longer time for lactose hydrolysis, enzyme cost for a liter
of lactose-free milk could be minimized. By using VYL at ½ the supplier recommended dosage
and allowing 72 hours for hydrolysis, cost could be as low as $0.05 per liter of milk. The price is
in addition to the normal processing costs of producing milk.
CONCLUSIONS
Commercially available lactase enzymes are active enough in chilled milk to enable the
hydrolysis process to be carried out during refrigerated storage. With the proper
time/concentration combinations, >99% lactose hydrolysis can be achieved. Sweetness in
lactose-free milk made by this method is acceptable as compared to current products on the
market. By reacting the milk during cold storage, the hydrolysis process can be simplified with
greater flexibility, potentially reducing the cost of manufacturing lactose-free milk.
13
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Harju, M., inventor; Valio Meijerien Keskusosuusliike, assignee. 1989 Apr 11. Process for the
specific separation of lactose from milk. U.S. patent 4,820,348.
Husain, Q. 2010. beta Galactosidases and their potential applications: a review. Critical Reviews
in Biotechnology 30(1):41-62.
Jelen, P. and O. Tossavainen. 2003. Low lactose and lactose-free milk and dairy products prospects, technologies and applications. Australian Journal of Dairy Technology
58(2):161-165.
Lopez, E. and R. A. Lopez. 2009. Demand for Differentiated Milk Products: Implications for
Price Competition. Agribusiness 25(4):453-465.
Mannion, C. A., K. Gray-Donald, and K. G. Koski. 2006. Association of low intake of milk and
vitamin D during pregnancy with decreased birth weight. Canadian Medical Association
Journal 174(9):1273-1277.
Messia, M. C., T. Candigliota, and E. Marconi. 2007. Assessment of quality and technological
characterization of lactose-hydrolyzed milk. Food Chemistry 104(3):910-917.
Mintel Oxygen. 2010. Milk – US – April 2010. London, UK: Mintel International Group
Limited.
Miller, J. H. 1972. Experiments in molecular genetics. Cold Spring Harbor, N.Y.: Cold Spring
Harbor Laboratory, Cold Spring Harbor, N.Y.].
Nielsen, S.S. 2003. Food Analysis. 3rd ed. New York, NY. Springer Science+Business Media,
Inc. 557 p.
Novalin, S., W. Neuhaus, and K. D. Kulbe. 2005. A new innovative process to produce lactosereduced skim milk. Journal of Biotechnology 119(2):212-218.
Panesar, R., P. S. Panesar, R. S. Singh, and M. B. Bera. 2007. Applicability of alginate entrapped
yeast cells for the production of lactose-hydrolyzed milk. Journal of Food Process
Engineering 30(4):472-484.
Schneider, R. E., E. Corona, F. Rosales, F. E. Schneider, O. Rodriguez, and O. Pineda. 1990.
Effect of temperature on the lactose hydrolytic capacity of a lactse derived from
Kluyveromyces-lactis. American Journal of Clinical Nutrition 51(2):197-201.
Sharma, R., Y. S. Rajput, Poonam, G. Dogra, and S. K. Tomar. 2009. Estimation of sugars in
milk by HPLC and its application in detection of adulteration of milk with soymilk.
International Journal of Dairy Technology 62(4):514-519.
15
Sieber, R., M. Stransky, and M. de Vrese. 1997. Lactose intolerance and consumption of milk
and dairy products. Zeitschrift Fur Ernahrungswissenschaft 36(4):375-393.
Somkuti, G. A. and V. H. Holsinger. 1997. Microbial technologies in the production of lowlactose dairy foods. Food Science and Technology International 3(3):163-169.
Switzer, R.L., and L.F. Garrity. 1999. Experimental biochemistry, theory and exercises in
fundamental methods. 3rd ed. New York NY: W H Freeman and Company. 453 p.
Wehr, H.M., and J.F. Frank. 2004. Standard methods for the examination of dairy products. 17th
ed. Washington DC: American Public Health Association. 570 p.
16
Figure 1 – Comparison of β-galactosidase activity of five commercial lactases at different temperatures.
Graph A shows the results expressed as change in optical density at 420 nm (ΔOD420) per minute per
volume of enzyme based on the adjusted Miller assay. Graph B shows the ΔOD420 per minute per mass
(ng) of protein for each enzyme. The mass of protein calculation adjusts for protein content of each
enzyme solution and allows for comparison of the efficiency of each enzyme preparation.
ΔOD420 per volume
A
β-Galactosidase Assay Results
3.0E+06
2.5E+06
2.0E+06
DYL
1.5E+06
VYL
1.0E+06
EYL
5.0E+05
LYL
VFL
0.0E+00
4⁰
10⁰
20⁰
ambient
Temperature (⁰C)
ΔOD420 per mass (ng) protein
B
Activity Adjusted for Protein Content
1.6
1.4
1.2
1
DYL
0.8
VYL
0.6
EYL
0.4
LYL
0.2
VFL
0
4⁰
10⁰
20⁰
Temperature (⁰C)
17
ambient
Figure 2 – Effects of milk type on enzyme performance of the LYL β-galactosidase at 2⁰C. Average
percent lactose hydrolysis is shown. Hydrolysis rate is very similar for all enzymes in all milk types.
Pasteurized Skim Milk
Percent Hydrolysis
120.00%
100.00%
80.00%
0.5x
60.00%
40.00%
1.0x
20.00%
1.5x
0.00%
2.0x
12
24
48
72
Hours
Pasteurized Whole Milk
Percent Hydrolysis
120.00%
100.00%
80.00%
0.5x
60.00%
40.00%
1.0x
20.00%
1.5x
0.00%
2.0x
12
24
48
72
Hours
Raw Whole Milk
Percent Hydrolysis
120.00%
100.00%
80.00%
0.5x
60.00%
40.00%
1.0x
20.00%
1.5x
0.00%
2.0x
12
24
48
Hours
18
72
Table 1 – Time-dependent lactose hydrolysis (2⁰C) in pasteurized whole milk for four selected
commercial enzymes at different concentrations. Concentrations represent the fraction of the suppliers’
recommended dosage used. The percentages listed in the table represent the average percent lactose
hydrolysis for the time/concentration pairs.
Enzyme
DYL
Concentration
Concentration
1/4x
1/2x
3/4x
1x
Hours
12
49.95%
75.36%
86.43%
92.78%
24
71.77%
89.38%
95.72%
99.08%
48
89.19%
98.55%
99.99%
99.99%
72
95.61%
99.70%
99.86%
99.99%
VYL
1/4x
1/2x
3/4x
1x
49.62%
67.34%
80.00%
90.13%
67.44%
88.90%
95.29%
98.59%
84.92%
98.27%
99.54%
99.99%
91.57%
99.43%
99.81%
99.99%
EYL
1/2x
1x
1.5x
2x
41.55%
62.29%
75.16%
85.86%
63.41%
85.23%
90.74%
97.32%
83.08%
96.67%
98.71%
99.99%
91.40%
99.05%
99.64%
99.99%
LYL
1/2x
1x
1.5x
2x
39.62%
61.36%
74.11%
82.37%
58.26%
82.96%
91.27%
95.89%
79.62%
96.39%
99.44%
99.99%
88.46%
98.94%
99.99%
99.99%
19
Table 2 – Mixed model statistics for lactose hydrolysis by four commercial enzymes after 24 and 72
hours, in whole milk at 2⁰C. The concentrations are based on the suppliers’ recommended dosage. The
statistics show the target levels of % lactose hydrolysis were achieved under the conditions indicated. A
p-value greater than 0.05 indicates the mean % hydrolysis and the target % hydrolysis are not
significantly different.
Enzyme
Concentration
DYL
VYL
EYL
LYL
1x
1x
2x
2x
Enzyme
Concentration
DYL
0.25x
0.5x
0.5x
1x
1x
VYL
EYL
LYL
Target %
Hydrolysis
99%
98%
95%
95%
24 Hours
Mean %
Hydrolysis
99.08%
99.59%
97.32%
95.89%
Standard
Error
2.75%
3.52%
1.81%
1.18%
p-value
Target %
Hydrolysis
95%
99%
99%
99%
99%
72 Hours
Mean %
Hydrolysis
95.61%
99.70%
99.43%
99.05%
98.94%
Standard
Error
2.75%
2.75%
3.52%
1.81%
1.18%
p-value
20
0.9715
0.8557
0.1876
0.2240
0.4780
0.9473
0.9900
0.5367
0.8319
Table 3 – Cost analysis for lactose hydrolysis in refrigerated milk (2⁰C) using the four β-galactosidase
enzymes evaluated in this study. Concentrations represent the fraction of the suppliers’ recommended
dosage required to achieve at least >95% lactose hydrolysis in the time allotted. Costs are for enzyme
only in addition to the normal costs of milk manufacture.
Minimum volume pricing of commercial enzymes per kg
DYL
$110.00
VYL
$100.00
EYL
$55.00
LYL
$63.22
Enzyme
DYL
Time/concentration
24 hour/1x
48 hour/0.75x
72 hour/0.5x
Cost per liter of milk
$0.11
$0.09
$0.06
Cost per kiloliter of milk
$113.59
$85.19
$56.80
VYL
24 hour/1x
48 hour/0.75x
72 hour/0.5x
$0.08
$0.08
$0.05
$82.61
$77.45
$51.63
EYL
24 hour/2x
48 hour/1.5x
72 hour/1x
$0.11
$0.08
$0.06
$112.62
$84.47
$56.31
LYL
24 hour/2x
48 hour/1.5x
72 hour/1x
$0.13
$0.10
$0.07
$130.57
$97.93
$65.28
21
APPENDICES
22
APPENDIX A
APPROVED PROSPECTUS
23
DEPARTMENT OF NUTRITION, DIETETICS AND FOOD SCIENCE
THESIS OR DISSERTATION PROSPECTUS
MASTER CANDIDATES
Proposed Title: Beta-Galactosidase Activity of Commercial Lactase Samples in Raw and
Pasteurized Milk at Refrigerated Temperatures.
Statement of the problem
Milk is a nutrient-dense food and an important part of a healthy diet. Along with good amounts
of high-quality protein, milk contains many vitamins and minerals, such as calcium, riboflavin,
and phosphorus. Milk is fortified with vitamin D and is one of the few food products containing
this vitamin. Unfortunately, many individuals are unable to consume milk due to lactoseintolerance and thus the benefits of milk are not readily available to them.
Lactose intolerance is caused by a deficiency of “lactase” (beta-galactosidase) in the digestive
tract. Normally, lactose in milk is hydrolyzed while in the intestinal tract. The lactose in milk is
broken down into glucose and galactose by the enzyme, and these monosaccharides are easily
utilized by the digestive system. When lactose intolerant individuals consume milk, the
undigested lactose passes into the colon and increases the osmolarity of digested food. This
inhibits the absorption of water by the colon and can cause diarrhea. Also, the bacteria in the
colon are able to digest the lactose which causes the acidity of the stools to increase and
produces gas and toxins. These unpleasant symptoms further inhibit the consumption of milk by
these individuals.
For those who are lactose-intolerant, lactose-reduced and lactose-free milk are available. These
milk products have 75-100% of the lactose removed. Normally, a β-galactosidase is used during
processing to break-down lactose into galactose and glucose which are easily digested.
However, the process for making this milk is expensive, and can cause the cost to be two-to-four
times the amount of normal milk. This higher price can be a problem for those who need the
milk, making it difficult for them to obtain the benefits that milk can give.
If β-galactosidase enzymes are determined to have sufficient activity in the cold to accomplish
hydrolysis in 24-72 hours, the reaction might be carried out during refrigeration storage and
thereby eliminating the expensive in-plant process. This would result in a lower overall cost of
producing lactose-reduced milk. The objective of this research was to determine if currently
available lactase enzymes were active enough in chilled milk to enable the hydrolysis process to
be carried out during refrigerated storage.
24
Method to be followed
There are two proposed methods for using potentially cold-active enzymes, outlined by the
following:
-Process milk as normal, adding sterile cold-active enzymes as the milk is packaged.
(Lactose hydrolysis would occur before being sold on store shelves)
-Add cold-active enzymes before milk arrives at the plant
(Adding the enzymes at the farm, before shipping to the plant)
Commercially available β-galactosidase enzymes were obtained. The temperature-activity
profiles of the enzymes were determined in milk at pH 6.8 using a rapid colorimetric assay. This
consisted of adding the candidate enzymes to a prepared assay buffer and reacting for several
minutes, recording the start time. The mixture produced a moderately yellow color, caused by
the hydrolysis of O-nitrophenyl-β, D-galactopyranoside (present in the assay buffer). Once the
yellow color was present, a stop buffer was added to halt the reaction and the stop time was
recorded. The mixture was then centrifuged and moved to a cuvette for use in a
spectrophotometer. The instrument was used to take a reading on the color of the mixture at OD
420nm, and the data gathered was used to calculate activity. This assay was performed at
various temperatures to produce the temperature vs. activity profile for each enzyme.
Candidate enzymes with cold-activity were reacted with milk using various concentrations at
2°C for 12, 24, 48, and 72 hour periods. Lactose content was determined at the end of the
reaction times by High Performance Liquid Chromatography (HPLC) to determine the extent of
hydrolysis. The times represented possible reaction times during cold-storage.
For HPLC analysis, the enzymes were denatured and milk samples were prepared using the
Lactose HPLC Method (Class B) 11(984.22), 50 (as referenced in Standard Methods for the
Examination of Dairy Products (2004)). Milk proteins were precipitated by adding 0.9N sulfuric
acid to each sample followed by centrifugation. Read-outs from the HPLC were checked against
galactose, glucose, and lactose standards.
Justification of the problem
The researched methods of reducing lactose in milk have the potential to save time and money.
Over-all, the enzymes would take more time at the lower temperatures, but this would be time
during shipping rather than time in the plant. The new methods require less employee time, less
plant space, and less energy. Potentially, such processes would be safer as well, since the milk
would stay at refrigeration temperatures during the entire process. It may also be possible to
eliminate the second pasteurization step, further saving time and money.
Feasibility of research for cheaper product includes the following:
-The market for lactose-reduced products is growing
-Jelen (2003) predicted about a 20% per year increase, due in part to increased
awareness of lactose intolerance
25
-Estimated market is about 50 million consumers (in U.S. alone)
Delimitations of the problem
Issues with lactose-reduced milk include factors such as a sweeter taste (from glucose and
galactose being sweeter than lactose) and potential off-flavors (potential for increased Maillard
browning with glucose/galactose during pasteurization). This study looked at these issues and
concluded that the milk produced by the researched methods was acceptable compared to
products currently on the market.
26
APPENDIX B
TESTING RELATIVE ACTIVITY OF THE ENZYMES: THE BETAGALACTOSIDASE ASSAY
27
Notes about the entire analysis – Please read first:
This analysis is adapted from the Miller Assay (Miller 1972), which is a bacterial assay.
In the bacterial assay, everything used must be sterile; however, sterility was not important for
testing these β-galactosidase enzymes. Also, the purified enzymes were much more active than a
broth of lactase producing bacteria. Thus, the enzymes were diluted (10-1 to 10-6) in order to
achieve similar results to the bacterial assay.
Preparation for the analysis – β-galactosidase reaction
Materials needed:
• 1.5 mL Microfuge tubes and rack for holding the tubes
• Basal Buffer
• Chloroform
• Assay Buffer
• Stop Buffer
• 2 Mechanical pipettes, one with 1mL tips and one with 100µL tips
• Stop watch or timer
1. Place 7 empty microfuge tubes in rack. The first 6 tubes are for each dilution (10-1 to 106
); the seventh tube is for making a blank.
2. Add 450µL of basal buffer to each tube.
3. Add 50µL of enzyme to the 450µL of basal buffer in the first microfuge tube (dilution 101
). Close the top of the tube and shake vigorously to mix well (at least 5 seconds of
shaking).
4. To each tube in succession, create dilutions of 10-2 through 10-6 by adding 50µL of the
previous dilution to the 450µL of basal buffer in the next tube and mix well (e.g. starting
with the first tube, take 50µL from the first tube and put it into the 450µL of basal buffer
in the second tube and mix).
5. For the blank, do not add any the enzyme to the tube.
6. Add 30µL of chloroform to each tube, including the blank.
7. Add 600µL of assay buffer to each dilution in order (including the blank). Close the top
of each tube and shake vigorously to mix well. Start the timer or record the start time
once the assay buffer is added to the first tube.
8. When samples are sufficiently yellow (produces a spectrophotometer reading between
0.1 and 1.0 at 420nm; I suggest using dilution 10-4 or 10-5), add 600 micro-liters of stop
buffer and mix well, stopping the timer or recording the stop time. The blank will not
turn yellow.
Running the analysis – Spectrophotometer
Materials needed:
•
•
•
Samples and blank from the β-galactosidase reaction (I found the 10-5 dilution worked
well)
A Centrifuge and test-tubes that fit the centrifuge
Cuvettes for each sample and the blank
28
•
Mechanical pipette with 1mL tips
1. Transfer the assay solutions to test tubes for use in a table-top centrifuge in Dr. Dunn’s
lab. Centrifuge the samples for at least a minute.
2. Transfer 1mL of each sample to cuvettes. Prepare the blank in the same manner.
3. Use the spectrophotometer in Dr. Dunn’s lab, set at 420nm and zeroed with the prepared
blank, to read the samples. Instructions for using the instrument are in appendix B-2.
Record the readings for each sample.
4. Plug the data into the equation (adapted for a non-bacterial assay), where OD420 is the
reading from the spectrophotometer:
Units per volume = [1000*OD420]/[volume(mL)*Time(min.)]
5. The units are useful for comparing enzyme activities. See figure 1 for the results of the
assay.
6. The data were adjusted to show ΔOD420 per mass of protein of enzyme, or efficiency of
the enzymes, as follows:
Units per mass = [OD420/(T)] * [Mass of protein(ng)] *1000
Where T = time in minutes and protein mass is calculated from the following:
Volume(ml)*(mg/ml of protein in the enzyme solution) * (dilution factor) * 10^6
Where volume is the amount of enzyme solution used in the assay (0.050 ml), dilution
factor being the dilution used for each trial (either 10^-4 or 10^-5), and 10^6 to convert
into nanograms.
29
Appendix B-1: Solutions
Basal Buffer
Materials needed:
• 500mL water
• 4.3 g NA2HPO4
• 2.4 g NaH2PO4
• 0.75 g KCL
• ~1.5mL 2N KOH
• 1mL of 1M MgSO4_7H2O
• 1 L autoclave bottle
Add the 500mL of water to the autoclave bottle. Add the NA2HPO4, NaH2PO4, and 0.75 g KCL
and mix well. The KOH is then added as needed to bring the pH up to 7.0 (it is possible the
solution will already be at pH 7.0 without adding KOH; in this case, don’t add the KOH).
Autoclave the solution. When cool, add the MgSO4_7H2O. Autoclave again. Store in
refrigerator to help prevent microbial growth after using.
Stop Buffer
Materials needed:
• 500mL water
• 1 M Na2CO3 (Sodium carbonate)
• 1 L autoclave bottle
Mix 53 g Na2CO3 with 500mL of water in the autoclave bottle. Autoclave (A precipitate may
form). Refrigerate to help prevent microbial growth after using.
Assay Buffer
Materials needed:
• 15 ml basal buffer
• 13.25 mg ONPG
• 11 µl 10% SDS (make 10% SDS solution by adding 10 g SDS to 90 g water)
• 45 µl β-mercaptoethanol (USE A VENT HOOD! It emits a strong, toxic sulfur smell)
• 100 ml flask
Add the basal buffer to the flask. Add the SDS solution and the β-mercaptoethanol (when
adding the β-mercaptoethanol, a vent hood must be used!). Add the ONPG, seal the flask,
and mix everything well (ONPG does not dissolve easily; it may be necessary to warm the
solution in order to get it to dissolve). Store in the refrigerator and keep it sealed while storing.
30
Appendix B-2: Spectrophotometer
Dr. Dunn lab Spectrophotometer (S-161 ESC)
Spectrophotometer model: Milton Roy Spectronic 1001 (Milton Roy Instrument Group)
1. Switch on the machine; wait for it to initialize the wavelength (WV)
2. Using the number pad, type in the desired wavelength (420) followed by pressing the “go
to λ” button. The machine will go to wavelength 420nm.
3. Open the samples’ compartment to the left of the display panel. Set the cuvettes in the
holders (be sure the clear side of the cuvettes correctly face the light source, which is
right of the sample holders). Place the prepared blank in first. Be sure to close the
compartment before taking any readings.
4. Zero the machine using the blank by pressing the “second function” button followed by
the “zero ABS” button. The display will revert to zero.
5. Use the knob and arm attached to the sample holders to move the next sample into place.
Record the data on the display panel, which should be between 0.1 and 1.0 for this assay.
6. Repeat the process for the remaining samples.
31
Appendix B-3: Explanation of the how the β-Galactosidase assay works
Source: Switzer RL, Garrity LF. 1999. Experimental biochemistry, theory and exercises in
fundamental methods. 3rd ed. New York: W H Freeman and Company. 453 p.
When O-nitrophenyl-β, D-Galactopyranoside (ONPG) reacts with a β-galactosidase enzyme,
galactose and O-Nitrophenol (ONP) are the products, and the solution turns a yellow color. ONP
absorbs light at 420nm in alkaline conditions, allowing for measurement by a spectrophotometer.
The gathered data can be put into the following equation (adapted from the original equation for
bacterial assays):
Activity Units = [1000*OD420]/[volume(mL)*Time(min.)]
OD420 is the reading from the spectrophotometer and time refers to the length of time in
minutes that the ONPG was reacted with the β-galactosidase during the assay.
Using the data from the Miller unit equation, the relative activity of the β-galactosidase enzymes
can be compared to one another, allowing for selection of the most effective enzymes.
32
APPENDIX C
HPLC ANALYSIS OF LACTOSE HYDROLYSIS
33
Preparation for the analysis – Lactose hydrolysis
Notes about this section: The instructions below were made using enzyme #1. The method
won’t change for the other enzymes other than the amount of enzyme used per 100 ml of milk
based on supplier instructions.
Materials needed:
•
•
•
100 ml milk
100 µl β-galactosidase
250 ml flask
1. Pour the milk into the flask and add the enzyme. Seal the flask and mix vigorously to
ensure thorough dispersion of the enzyme.
2. Place the flask in a refrigerator for the proper amount of hours according to the
experimental design.
3. Remove from refrigerator and HTST pasteurize the sample (161⁰C for 15 seconds) in
order to denature the enzyme. Cool the pasteurized sample in refrigerator to prepare for
the next step.
Preparation for the analysis – Separation of milk proteins
Materials needed:
•
•
•
•
•
•
•
•
•
100 ml volumetric flask
10 g pasteurized milk sample from previous step
Analytical scale
Pasteur pipettes
1 ml 0.9N sulfuric acid
Distilled-deionized water
3 ml syringes with attached syringe filters, 0.45 µm
HPLC vials with caps
A capper to seal HPLC vials
1.
2.
3.
4.
5.
Place the flask on the analytical balance and tare the weight.
Measure 10.0000 ± 0.0030 g milk into the flask.
Remove flask from balance, add 1 ml sulfuric acid to the milk and swirl.
Add ~50 ml of the water to the flask and swirl again.
Bring the mixture to volume (100 ml) with water and seal the flask. Shake vigorously for
20 seconds.
6. Let the mixture to stand for at least 5 minutes to allow good separation of the proteins
from the liquid fraction. A layer of white milk proteins will settle out on the bottom of
the flask.
7. Use a Pasteur pipette to remove the liquid fraction of the milk and put the liquid into a
syringe w/filter attached. Two pipettes of liquid should be plenty.
8. Use the syringe to filter the liquid into an HPLC vial. Fill the vial at least half-full and no
more than ¾ full.
34
9. Cap and seal the vial.
Source:
Wehr MH, Frank JF. 2004. Standard Methods for the examination of dairy products. 17th ed.
Washington DC: American Public Health Association.
35
Appendix C-1: Solutions
0.9N Sulfuric Acid
Materials needed:
• 100mL volumetric flask
• A separate flask/beaker/bottle for storage
• Concentrated sulfuric acid (10M)
Add 9mL of 10M sulfuric acid to the flask. Bring up to volume with distilled-deionized water.
Store the acid in a separate flask to enable easy access to the acid using Pasteur pipettes.
36
Appendix C-2: Results of HPLC Analysis
This appendix contains the raw data from the HPLC analysis of all the milk samples.
Each page contains one of the six trials from the three types of milk experimented upon, denoted
by the label at the top of the page.
The tables on the top of each page contain the percent lactose hydrolysis of every sample
(384 samples total). Underneath the tables are graphical summaries of the data in the tables.
The legend on each graph shows the concentration of each enzyme.
Each table is organized with time (hours) at the top of each column and the concentration
of each enzyme in the left column under the enzyme designation.
Figure 1 Skim Milk Trial #1 ......................................................................................................... 38
Figure 2 Skim Milk Trial #2 ......................................................................................................... 39
Figure 3 Whole Milk Trial #1 ....................................................................................................... 40
Figure 4 Whole Milk Trial #2 ....................................................................................................... 41
Figure 5 Raw Milk Trial #1 .......................................................................................................... 42
Figure 6 Raw Milk Trial #2 .......................................................................................................... 43
37
DYL
0.25x
0.5x
0.75x
1.0x
Percent Hydrolysis
12
24
48
35.39% 61.60% 81.16%
76.75% 87.95% 97.93%
84.85% 92.37% 99.99%
94.71%
99% 99.99%
72
91.36%
99.99%
99.99%
99.99%
EYL
0.5x
1.0x
1.5x
2.0x
12
31.75%
58.52%
72.79%
85.60%
24
60.24%
92.64%
96.60%
97.03%
48
82.87%
98.13%
98.76%
99.99%
72
93.24%
99.99%
99.99%
99.99%
VYL
0.25x
0.5x
0.75x
1.0x
12
42.86%
59.82%
77.84%
87.48%
72
96.60%
99.99%
99.99%
99.99%
LYL
0.5x
1.0x
1.5x
2.0x
12
39.03%
61.11%
74.04%
79.72%
24
58.21%
81.82%
91.81%
96.78%
48
79.67%
96.50%
99.99%
99.99%
72
88.48%
98.52%
99.99%
99.99%
24
75.97%
89.51%
96.70%
98.07%
48
89.58%
98.84%
99.99%
99.99%
DYL
EYL
120.00%
Percent Hydrolysis
Percent Hydrolysis
120.00%
100.00%
80.00%
1.0x
60.00%
40.00%
0.75x
20.00%
0.5x
0.00%
0.25x
12
24
48
100.00%
80.00%
2.0x
60.00%
40.00%
1.5x
20.00%
1.0x
0.00%
0.5x
72
12
Hours
48
72
Hours
VYL
LYL
120.00%
Percent Hydrolysis
120.00%
Percent Hydrolysis
24
100.00%
80.00%
1.0x
60.00%
40.00%
0.75x
20.00%
0.5x
0.00%
0.25x
12
24
48
72
100.00%
80.00%
2.0x
60.00%
40.00%
1.5x
20.00%
1.0x
0.00%
0.5x
12
Hours
24
48
Hours
Figure 1 Skim Milk Trial #1
38
72
DYL
1/4x
1/2x
3/4x
1x
Percent Hydrolysis
12
24
48
40.10% 63.75% 84.67%
69.61% 86.68% 99.81%
84.49% 96.17% 99.99%
90.17% 98.08% 99.99%
72
93.26%
99.86%
99.99%
99.99%
EYL
1/2x
1x
1.5x
2x
12
36.61%
60.15%
73.87%
85.78%
24
58.29%
81.21%
88.45%
97.52%
48
79.99%
95.60%
99.15%
99.99%
72
89.57%
99.70%
99.99%
99.99%
VYL
1/4x
1/2x
3/4x
1x
12
32.81%
67.25%
71.51%
86.12%
72
88.43%
99.99%
99.99%
99.99%
LYL
1/2x
1x
1.5x
2x
12
35.34%
60.22%
73.78%
81.83%
24
57.46%
83.96%
89.26%
94.20%
48
77.80%
96.01%
98.74%
99.99%
72
89.48%
99.63%
99.99%
99.99%
24
60.47%
86.06%
92.46%
98.39%
48
79.31%
96.50%
98.89%
99.99%
DYL
EYL
120.00%
Percent Hydrolysis
Percent Hydrolysis
120.00%
100.00%
80.00%
1.0x
60.00%
40.00%
0.75x
20.00%
0.5x
0.00%
0.25x
12
24
48
100.00%
80.00%
2.0x
60.00%
40.00%
1.5x
20.00%
1.0x
0.00%
0.5x
72
12
Hours
48
72
Hours
VYL
LYL
120.00%
Percent Hydrolysis
120.00%
Percent Hydrolysis
24
100.00%
80.00%
1.0x
60.00%
40.00%
0.75x
20.00%
0.5x
0.00%
0.25x
12
24
48
72
100.00%
80.00%
2.0x
60.00%
40.00%
1.5x
20.00%
1.0x
0.00%
0.5x
12
Hours
24
48
Hours
Figure 2 Skim Milk Trial #2
39
72
DYL
1/4x
1/2x
3/4x
1x
Percent Hydrolysis
12
24
48
51.64% 78.53% 94.24%
71.34% 89.38% 98.57%
86.56% 97.26% 99.99%
94.29% 99.99% 99.99%
72
97.03%
99.09%
99.99%
99.99%
EYL
1/2x
1x
1.5x
2x
12
42.86%
60.49%
81.69%
88.25%
24
65.08%
85.87%
93.26%
98.57%
48
86.87%
97.29%
99.46%
99.99%
72
92.94%
99.01%
99.99%
99.99%
VYL
1/4x
1/2x
3/4x
1x
12
54.79%
66.47%
83.34%
93.40%
72
86.27%
99.99%
99.99%
99.99%
LYL
1/2x
1x
1.5x
2x
12
41.87%
64.87%
75.37%
84.68%
24
58.75%
87.29%
94.24%
96.41%
48
80.83%
98.56%
99.99%
99.99%
72
88.10%
99.46%
99.99%
99.99%
24
55.86%
88.46%
93.52%
99.14%
48
77.80%
98.49%
99.99%
99.99%
DYL
EYL
120.00%
Percent Hydrolysis
Percent Hydrolysis
120.00%
100.00%
80.00%
1.0x
60.00%
40.00%
0.75x
20.00%
0.5x
0.00%
0.25x
12
24
48
100.00%
80.00%
2.0x
60.00%
40.00%
1.5x
20.00%
1.0x
0.00%
0.5x
72
12
Hours
48
72
Hours
VYL
LYL
120.00%
Percent Hydrolysis
120.00%
Percent Hydrolysis
24
100.00%
80.00%
1.0x
60.00%
40.00%
0.75x
20.00%
0.5x
0.00%
0.25x
12
24
48
72
100.00%
80.00%
2.0x
60.00%
40.00%
1.5x
20.00%
1.0x
0.00%
0.5x
12
Hours
24
48
Hours
Figure 3 Whole Milk Trial #1
40
72
DYL
1/4x
1/2x
3/4x
1x
Percent Hydrolysis
12
24
48
66.44% 75.87% 92.08%
86.83% 90.35% 98.13%
88.53% 96.39% 99.99%
92.14% 98.21% 99.99%
72
96.97%
99.28%
99.18%
99.99%
EYL
1/2x
1x
1.5x
2x
12
53.16%
66.98%
78.94%
84.24%
24
64.78%
83.81%
93.23%
96.40%
48
84.37%
95.97%
98.96%
99.99%
72
89.83%
96.71%
97.87%
99.99%
VYL
1/4x
1/2x
3/4x
1x
12
69.91%
77.23%
84.59%
93.69%
72
92.23%
97.92%
98.89%
99.99%
LYL
1/2x
1x
1.5x
2x
12
42.49%
60.45%
76.74%
81.81%
24
63.19%
83.01%
92.26%
96.58%
48
83.79%
96.20%
99.41%
99.99%
72
88.91%
98.03%
99.99%
99.99%
24
72.77%
85.21%
96.70%
98.16%
48
87.65%
98.00%
99.99%
99.99%
DYL
EYL
120.00%
Percent Hydrolysis
Percent Hydrolysis
120.00%
100.00%
80.00%
1.0x
60.00%
40.00%
0.75x
20.00%
0.5x
0.00%
0.25x
12
24
48
100.00%
80.00%
2.0x
60.00%
40.00%
1.5x
20.00%
1.0x
0.00%
0.5x
72
12
Hours
48
72
Hours
VYL
LYL
120.00%
Percent Hydrolysis
120.00%
Percent Hydrolysis
24
100.00%
80.00%
1.0x
60.00%
40.00%
0.75x
20.00%
0.5x
0.00%
0.25x
12
24
48
72
100.00%
80.00%
2.0x
60.00%
40.00%
1.5x
20.00%
1.0x
0.00%
0.5x
12
Hours
24
48
Hours
Figure 4 Whole Milk Trial #2
41
72
DYL
1/4x
1/2x
3/4x
1x
Percent Hydrolysis
12
24
48
54.07% 73.23% 90.57%
72.47% 91.44% 98.83%
88.08% 97.13% 99.99%
93.09% 99.99% 99.99%
72
97.87%
99.99%
99.99%
99.99%
EYL
1/2x
1x
1.5x
2x
12
39.30%
64.79%
64.32%
86.30%
24
64.57%
84.89%
81.33%
97.66%
48
77.31%
96.42%
97.09%
99.99%
72
87.74%
99.14%
99.99%
99.99%
VYL
1/4x
1/2x
3/4x
1x
12
43.39%
61.45%
83.76%
91.07%
72
93.86%
99.99%
99.99%
99.99%
LYL
1/2x
1x
1.5x
2x
12
37.71%
56.55%
72.94%
84.11%
24
55.78%
78.71%
89.66%
96.25%
48
76.93%
93.83%
98.67%
99.99%
72
87.53%
98.00%
99.99%
99.99%
24
73.62%
95.47%
97.56%
98.71%
48
89.58%
99.99%
99.99%
99.99%
DYL
EYL
120.00%
Percent Hydrolysis
Percent Hydrolysis
120.00%
100.00%
80.00%
1.0x
60.00%
40.00%
0.75x
20.00%
0.5x
0.00%
0.25x
12
24
48
100.00%
80.00%
2.0x
60.00%
40.00%
1.5x
20.00%
1.0x
0.00%
0.5x
72
12
Hours
48
72
Hours
VYL
LYL
120.00%
Percent Hydrolysis
120.00%
Percent Hydrolysis
24
100.00%
80.00%
1.0x
60.00%
40.00%
0.75x
20.00%
0.5x
0.00%
0.25x
12
24
48
72
100.00%
80.00%
2.0x
60.00%
40.00%
1.5x
20.00%
1.0x
0.00%
0.5x
12
Hours
24
48
Hours
Figure 5 Raw Milk Trial #1
42
72
DYL
1/4x
1/2x
3/4x
1x
Percent Hydrolysis
12
24
48
52.03% 77.64% 92.43%
75.16% 90.46% 98.05%
86.04% 94.98% 99.99%
92.28% 98.19% 99.99%
72
97.19%
99.99%
99.99%
99.99%
EYL
1/2x
1x
1.5x
2x
12
45.60%
62.83%
79.37%
84.96%
24
67.48%
82.98%
91.59%
96.72%
48
87.06%
96.60%
98.84%
99.99%
72
95.10%
99.73%
99.99%
99.99%
VYL
1/4x
1/2x
3/4x
1x
12
53.93%
71.80%
78.93%
89.00%
72
92.05%
98.68%
99.99%
99.99%
LYL
1/2x
1x
1.5x
2x
12
41.25%
64.95%
71.80%
82.06%
24
56.14%
82.94%
90.41%
95.11%
48
78.72%
97.21%
99.86%
99.99%
72
88.27%
99.99%
99.99%
99.99%
24
65.95%
88.70%
94.77%
99.07%
48
85.60%
97.82%
98.38%
99.99%
DYL
EYL
120.00%
Percent Hydrolysis
Percent Hydrolysis
120.00%
100.00%
80.00%
1.0x
60.00%
40.00%
0.75x
20.00%
0.5x
0.00%
0.25x
12
24
48
100.00%
80.00%
2.0x
60.00%
40.00%
1.5x
20.00%
1.0x
0.00%
0.5x
72
12
Hours
48
72
Hours
VYL
LYL
120.00%
Percent Hydrolysis
120.00%
Percent Hydrolysis
24
100.00%
80.00%
1.0x
60.00%
40.00%
0.75x
20.00%
0.5x
0.00%
0.25x
12
24
48
72
100.00%
80.00%
2.0x
60.00%
40.00%
1.5x
20.00%
1.0x
0.00%
0.5x
12
Hours
24
48
Hours
Figure 6 Raw Milk Trial #2
43
72
APPENDIX D
STATISTICAL ANALYSIS OF HPLC DATA
44
Statistics, calculated using SAS version 9.2, for the analysis of the HPLC data on hydrolysis of lactose
are included in this appendix. The SAS code used is listed below. The data was originally pulled
from an excel file; this data is found in appendix C-2. The statistical analysis was run based on a
lactose hydrolysis of 95%, 98%, and 99%.
PROC IMPORT OUT= WORK.in
DATAFILE= "C:\SAS\bioag\fsn\ogden\horner\lactase.xls"
DBMS=EXCEL REPLACE;
RANGE="Sheet1$";
GETNAMES=YES;
MIXED=NO;
SCANTEXT=YES;
USEDATE=YES;
SCANTIME=YES;
run;
*Enzyme Time Concentration Hydrolysis Milk Trial;
title2 'difference from .95';
data good;set in;
zeroed=.95-hydrolysis;
run;
proc sort data=good;
by enzyme milk;
proc mixed data=good;
class time concentration;
model zeroed=time concentration time*concentration;
lsmeans time*concentration;
by enzyme milk;
run;
45
The SAS System
14:28 Friday, February 19, 2010
difference from .95
------------------------------------ Enzyme=Danisco Milk=raw ------------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Time
Concentration
4
4
Values
12 24 48 72
0.25 0.5 0.75 1
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000153
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
46
-84.0
-82.0
-81.8
The SAS System
14:28 Friday, February 19, 2010
difference from .95
------------------------------------ Enzyme=Danisco Milk=raw ------------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-81.3
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
554.23
358.67
71.37
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.4195
0.2119
0.07940
0.02315
0.1957
0.04050
-0.01055
-0.04090
0.03500
-0.03440
-0.04990
-0.04990
-0.02530
-0.04990
-0.04990
-0.04990
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
47.93
24.21
9.07
2.65
22.36
4.63
-1.21
-4.67
4.00
-3.93
-5.70
-5.70
-2.89
-5.70
-5.70
-5.70
<.0001
<.0001
<.0001
0.0176
<.0001
0.0003
0.2455
0.0003
0.0010
0.0012
<.0001
<.0001
0.0106
<.0001
<.0001
<.0001
47
The SAS System
14:28 Friday, February 19, 2010
difference from .95
------------------------------------ Enzyme=Danisco Milk=skim -----------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Time
Concentration
4
4
Values
12 24 48 72
0.25 0.5 0.75 1
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000422
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
-67.8
-65.8
-65.6
The SAS System
14:28 Friday, February 19, 2010
difference from .95
------------------------------------ Enzyme=Danisco Milk=skim -----------------------------------The Mixed Procedure
Fit Statistics
48
BIC (smaller is better)
-65.1
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
263.96
321.14
39.40
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.5725
0.2182
0.1033
0.02560
0.3233
0.07685
0.007300
-0.03540
0.1208
-0.03870
-0.04990
-0.04990
0.02690
-0.04925
-0.04990
-0.04990
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
39.44
15.03
7.11
1.76
22.26
5.29
0.50
-2.44
8.32
-2.67
-3.44
-3.44
1.85
-3.39
-3.44
-3.44
<.0001
<.0001
<.0001
0.0969
<.0001
<.0001
0.6220
0.0268
<.0001
0.0169
0.0034
0.0034
0.0825
0.0037
0.0034
0.0034
49
The SAS System
14:28 Friday, February 19, 2010
difference from .95
----------------------------------- Enzyme=Danisco Milk=whole -----------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Time
Concentration
4
4
Values
12 24 48 72
0.25 0.5 0.75 1
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.001516
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
-47.4
-45.4
-45.1
The SAS System
14:28 Friday, February 19, 2010
difference from .95
----------------------------------- Enzyme=Danisco Milk=whole -----------------------------------The Mixed Procedure
Fit Statistics
50
BIC (smaller is better)
-44.6
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
41.32
28.32
5.21
<.0001
<.0001
0.0021
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.3596
0.1591
0.07455
0.01785
0.1780
0.05135
-0.01825
-0.04100
0.01840
-0.03350
-0.04990
-0.04990
-0.02000
-0.04185
-0.04585
-0.04990
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
13.06
5.78
2.71
0.65
6.47
1.87
-0.66
-1.49
0.67
-1.22
-1.81
-1.81
-0.73
-1.52
-1.67
-1.81
<.0001
<.0001
0.0155
0.5259
<.0001
0.0806
0.5168
0.1558
0.5134
0.2413
0.0887
0.0887
0.4780
0.1480
0.1153
0.0887
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
51
The SAS System
14:28 Friday, February 19, 2010
difference from .95
------------------------------------- Enzyme=Enzeco Milk=raw ------------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Values
4
4
12 24 48 72
0.5 1 1.5 2
Time
Concentration
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.001696
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
52
-45.6
-43.6
-43.3
The SAS System
14:28 Friday, February 19, 2010
difference from .95
------------------------------------- Enzyme=Enzeco Milk=raw ------------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-42.8
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
96.09
53.64
4.80
<.0001
<.0001
0.0032
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.5255
0.3119
0.2316
0.09370
0.2897
0.1106
0.08540
-0.02190
0.1281
-0.01510
-0.02965
-0.04990
0.03580
-0.04435
-0.04990
-0.04990
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
18.04
10.71
7.95
3.22
9.95
3.80
2.93
-0.75
4.40
-0.52
-1.02
-1.71
1.23
-1.52
-1.71
-1.71
<.0001
<.0001
<.0001
0.0054
<.0001
0.0016
0.0098
0.4630
0.0004
0.6112
0.3238
0.1059
0.2367
0.1473
0.1059
0.1059
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
53
The SAS System
14:28 Friday, February 19, 2010
difference from .95
------------------------------------ Enzyme=Enzeco Milk=skim ------------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Values
4
4
12 24 48 72
0.5 1 1.5 2
Time
Concentration
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000803
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
54
-57.5
-55.5
-55.3
The SAS System
14:28 Friday, February 19, 2010
difference from .95
------------------------------------ Enzyme=Enzeco Milk=skim ------------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-54.8
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
242.30
163.96
17.73
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.6082
0.3567
0.2167
0.09310
0.3574
0.08075
0.02475
-0.02275
0.1357
-0.01865
-0.03955
-0.04990
0.03595
-0.04845
-0.04990
-0.04990
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
30.35
17.80
10.81
4.65
17.83
4.03
1.24
-1.14
6.77
-0.93
-1.97
-2.49
1.79
-2.42
-2.49
-2.49
<.0001
<.0001
<.0001
0.0003
<.0001
0.0010
0.2346
0.2730
<.0001
0.3658
0.0659
0.0241
0.0917
0.0279
0.0241
0.0241
55
The SAS System
14:28 Friday, February 19, 2010
difference from .95
------------------------------------ Enzyme=Enzeco Milk=whole -----------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Values
4
4
12 24 48 72
0.5 1 1.5 2
Time
Concentration
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000652
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
-60.9
-58.9
-58.6
The SAS System
14:28 Friday, February 19, 2010
difference from .95
------------------------------------ Enzyme=Enzeco Milk=whole -----------------------------------The Mixed Procedure
Fit Statistics
56
BIC (smaller is better)
-58.1
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
195.40
133.68
13.28
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.4699
0.3127
0.1469
0.08755
0.3007
0.1016
0.01755
-0.02485
0.09380
-0.01630
-0.04210
-0.04990
0.03615
-0.02860
-0.03930
-0.04990
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
26.03
17.32
8.13
4.85
16.66
5.63
0.97
-1.38
5.20
-0.90
-2.33
-2.76
2.00
-1.58
-2.18
-2.76
<.0001
<.0001
<.0001
0.0002
<.0001
<.0001
0.3455
0.1876
<.0001
0.3800
0.0331
0.0138
0.0625
0.1327
0.0448
0.0138
57
The SAS System
14:28 Friday, February 19, 2010
difference from .95
------------------------------------- Enzyme=Sigma Milk=raw -------------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Values
4
4
12 24 48 72
0.5 1 1.5 2
Time
Concentration
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000403
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
-68.6
-66.6
-66.3
The SAS System
14:28 Friday, February 19, 2010
difference from .95
------------------------------------- Enzyme=Sigma Milk=raw -------------------------------------The Mixed Procedure
Fit Statistics
58
BIC (smaller is better)
-65.8
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
436.09
333.80
20.93
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.5552
0.3425
0.2263
0.1191
0.3904
0.1417
0.04965
-0.00680
0.1718
-0.00520
-0.04265
-0.04990
0.07100
-0.03995
-0.04990
-0.04990
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
39.10
24.12
15.94
8.39
27.49
9.98
3.50
-0.48
12.10
-0.37
-3.00
-3.51
5.00
-2.81
-3.51
-3.51
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.0030
0.6385
<.0001
0.7190
0.0084
0.0029
0.0001
0.0125
0.0029
0.0029
59
The SAS System
14:28 Friday, February 19, 2010
difference from .95
------------------------------------- Enzyme=Sigma Milk=skim ------------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Values
4
4
12 24 48 72
0.5 1 1.5 2
Time
Concentration
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000140
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
60
-85.5
-83.5
-83.2
The SAS System
14:28 Friday, February 19, 2010
difference from .95
------------------------------------- Enzyme=Sigma Milk=skim ------------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-82.7
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
1337.92
925.49
62.39
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.5782
0.3434
0.2109
0.1423
0.3717
0.1211
0.04465
-0.00490
0.1626
-0.01255
-0.04365
-0.04990
0.06020
-0.04075
-0.04990
-0.04990
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
69.13
41.06
25.22
17.01
44.44
14.48
5.34
-0.59
19.45
-1.50
-5.22
-5.97
7.20
-4.87
-5.97
-5.97
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.5661
<.0001
0.1529
<.0001
<.0001
<.0001
0.0002
<.0001
<.0001
61
The SAS System
14:28 Friday, February 19, 2010
difference from .95
------------------------------------ Enzyme=Sigma Milk=whole ------------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Values
4
4
12 24 48 72
0.5 1 1.5 2
Time
Concentration
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000279
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
-74.4
-72.4
-72.1
The SAS System
14:28 Friday, February 19, 2010
difference from .95
------------------------------------ Enzyme=Sigma Milk=whole ------------------------------------The Mixed Procedure
Fit Statistics
62
BIC (smaller is better)
-71.7
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
569.37
404.76
28.73
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.5282
0.3234
0.1894
0.1175
0.3403
0.09850
0.01750
-0.01495
0.1269
-0.02380
-0.04700
-0.04990
0.06495
-0.03745
-0.04990
-0.04990
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
44.69
27.37
16.03
9.95
28.80
8.33
1.48
-1.27
10.74
-2.01
-3.98
-4.22
5.50
-3.17
-4.22
-4.22
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.1581
0.2240
<.0001
0.0612
0.0011
0.0006
<.0001
0.0060
0.0006
0.0006
63
The SAS System
14:28 Friday, February 19, 2010
difference from .95
------------------------------------ Enzyme=Validase Milk=raw -----------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Time
Concentration
4
4
Values
12 24 48 72
0.25 0.5 0.75 1
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.001208
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
64
-51.0
-49.0
-48.7
The SAS System
14:28 Friday, February 19, 2010
difference from .95
------------------------------------ Enzyme=Validase Milk=raw -----------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-48.2
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
96.62
65.68
8.52
<.0001
<.0001
0.0001
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.4634
0.2838
0.1366
0.04965
0.2522
0.02915
-0.01165
-0.03890
0.07410
-0.03905
-0.04185
-0.04990
0.02045
-0.04335
-0.04990
-0.04990
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
18.86
11.55
5.56
2.02
10.26
1.19
-0.47
-1.58
3.02
-1.59
-1.70
-2.03
0.83
-1.76
-2.03
-2.03
<.0001
<.0001
<.0001
0.0604
<.0001
0.2529
0.6419
0.1330
0.0082
0.1316
0.1079
0.0593
0.4176
0.0968
0.0593
0.0593
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
65
The SAS System
14:28 Friday, February 19, 2010
difference from .95
----------------------------------- Enzyme=Validase Milk=skim -----------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Time
Concentration
4
4
Values
12 24 48 72
0.25 0.5 0.75 1
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.002023
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
66
-42.8
-40.8
-40.5
The SAS System
14:28 Friday, February 19, 2010
difference from .95
----------------------------------- Enzyme=Validase Milk=skim -----------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-40.0
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
85.25
49.53
5.99
<.0001
<.0001
0.0010
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.5717
0.3146
0.2032
0.08200
0.2678
0.07215
0.004200
-0.03230
0.1055
-0.02670
-0.04440
-0.04990
0.02485
-0.04990
-0.04990
-0.04990
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
17.98
9.89
6.39
2.58
8.42
2.27
0.13
-1.02
3.32
-0.84
-1.40
-1.57
0.78
-1.57
-1.57
-1.57
<.0001
<.0001
<.0001
0.0202
<.0001
0.0375
0.8966
0.3249
0.0043
0.4135
0.1817
0.1362
0.4460
0.1362
0.1362
0.1362
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
67
The SAS System
14:28 Friday, February 19, 2010
difference from .95
----------------------------------- Enzyme=Validase Milk=whole ----------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Time
Concentration
4
4
Values
12 24 48 72
0.25 0.5 0.75 1
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.002475
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
-39.5
-37.5
-37.2
The SAS System
14:28 Friday, February 19, 2010
difference from .95
----------------------------------- Enzyme=Validase Milk=whole ----------------------------------The Mixed Procedure
Fit Statistics
68
BIC (smaller is better)
-36.8
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
24.97
34.38
2.58
<.0001
<.0001
0.0473
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.3265
0.2315
0.1103
0.01455
0.3068
0.08165
-0.00110
-0.03650
0.1227
-0.03245
-0.04990
-0.04990
0.05750
-0.03955
-0.04440
-0.04990
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
9.28
6.58
3.14
0.41
8.72
2.32
-0.03
-1.04
3.49
-0.92
-1.42
-1.42
1.63
-1.12
-1.26
-1.42
<.0001
<.0001
0.0064
0.6846
<.0001
0.0338
0.9754
0.3149
0.0030
0.3700
0.1752
0.1752
0.1216
0.2775
0.2250
0.1752
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
69
The SAS System
14:28 Friday, February 19, 2010
difference from .98
------------------------------------ Enzyme=Dansico Milk=raw ------------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Time
Concentration
4
4
Values
12 24 48 72
0.25 0.5 0.75 1
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000153
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
70
-84.0
-82.0
-81.8
The SAS System
14:28 Friday, February 19, 2010
difference from .98
------------------------------------ Enzyme=Dansico Milk=raw ------------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-81.3
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
554.23
358.67
71.37
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.4495
0.2419
0.1094
0.05315
0.2257
0.07050
0.01945
-0.01090
0.06500
-0.00440
-0.01990
-0.01990
0.004700
-0.01990
-0.01990
-0.01990
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
51.36
27.64
12.50
6.07
25.78
8.06
2.22
-1.25
7.43
-0.50
-2.27
-2.27
0.54
-2.27
-2.27
-2.27
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.0410
0.2309
<.0001
0.6220
0.0371
0.0371
0.5986
0.0371
0.0371
0.0371
71
The SAS System
14:28 Friday, February 19, 2010
difference from .98
------------------------------------ Enzyme=Dansico Milk=skim -----------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Time
Concentration
4
4
Values
12 24 48 72
0.25 0.5 0.75 1
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000422
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
-67.8
-65.8
-65.6
The SAS System
14:28 Friday, February 19, 2010
difference from .98
------------------------------------ Enzyme=Dansico Milk=skim -----------------------------------The Mixed Procedure
Fit Statistics
72
BIC (smaller is better)
-65.1
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
263.96
321.14
39.40
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.6026
0.2482
0.1333
0.05560
0.3533
0.1069
0.03730
-0.00540
0.1509
-0.00870
-0.01990
-0.01990
0.05690
-0.01925
-0.01990
-0.01990
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
41.50
17.10
9.18
3.83
24.33
7.36
2.57
-0.37
10.39
-0.60
-1.37
-1.37
3.92
-1.33
-1.37
-1.37
<.0001
<.0001
<.0001
0.0015
<.0001
<.0001
0.0206
0.7148
<.0001
0.5574
0.1894
0.1894
0.0012
0.2035
0.1894
0.1894
73
The SAS System
14:28 Friday, February 19, 2010 difference from .98
----------------------------------- Enzyme=Dansico Milk=whole -----------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Time
Concentration
4
4
Values
12 24 48 72
0.25 0.5 0.75 1
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.001516
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
74
-47.4
-45.4
-45.1
The SAS System
14:28 Friday, February 19, 2010
difference from .98
----------------------------------- Enzyme=Dansico Milk=whole -----------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-44.6
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
41.32
28.32
5.21
<.0001
<.0001
0.0021
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.3896
0.1892
0.1045
0.04785
0.2080
0.08135
0.01175
-0.01100
0.04840
-0.00350
-0.01990
-0.01990
0.01000
-0.01185
-0.01585
-0.01990
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
14.15
6.87
3.80
1.74
7.56
2.96
0.43
-0.40
1.76
-0.13
-0.72
-0.72
0.36
-0.43
-0.58
-0.72
<.0001
<.0001
0.0016
0.1014
<.0001
0.0093
0.6752
0.6947
0.0978
0.9004
0.4802
0.4802
0.7212
0.6726
0.5728
0.4802
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
75
The SAS System
14:28 Friday, February 19, 2010
difference from .98
------------------------------------- Enzyme=Enzeco Milk=raw ------------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Values
4
4
12 24 48 72
0.5 1 1.5 2
Time
Concentration
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.001696
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
-45.6
-43.6
-43.3
The SAS System
14:28 Friday, February 19, 2010
difference from .98
------------------------------------- Enzyme=Enzeco Milk=raw ------------------------------------The Mixed Procedure
Fit Statistics
76
BIC (smaller is better)
-42.8
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
96.09
53.64
4.80
<.0001
<.0001
0.0032
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.5555
0.3419
0.2616
0.1237
0.3198
0.1407
0.1154
0.008100
0.1581
0.01490
0.000350
-0.01990
0.06580
-0.01435
-0.01990
-0.01990
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
19.08
11.74
8.98
4.25
10.98
4.83
3.96
0.28
5.43
0.51
0.01
-0.68
2.26
-0.49
-0.68
-0.68
<.0001
<.0001
<.0001
0.0006
<.0001
0.0002
0.0011
0.7845
<.0001
0.6159
0.9906
0.5042
0.0382
0.6289
0.5042
0.5042
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
77
The SAS System
14:28 Friday, February 19, 2010
difference from .98
------------------------------------ Enzyme=Enzeco Milk=skim ------------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Values
4
4
12 24 48 72
0.5 1 1.5 2
Time
Concentration
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000803
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
-57.5
-55.5
-55.3
The SAS System
14:28 Friday, February 19, 2010
difference from .98
------------------------------------ Enzyme=Enzeco Milk=skim ------------------------------------The Mixed Procedure
Fit Statistics
78
BIC (smaller is better)
-54.8
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
242.30
163.96
17.73
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.6382
0.3867
0.2467
0.1231
0.3874
0.1107
0.05475
0.007250
0.1657
0.01135
-0.00955
-0.01990
0.06595
-0.01845
-0.01990
-0.01990
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
31.85
19.30
12.31
6.14
19.33
5.53
2.73
0.36
8.27
0.57
-0.48
-0.99
3.29
-0.92
-0.99
-0.99
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.0148
0.7222
<.0001
0.5790
0.6401
0.3354
0.0046
0.3709
0.3354
0.3354
79
The SAS System
14:28 Friday, February 19, 2010
difference from .98
------------------------------------ Enzyme=Enzeco Milk=whole -----------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Values
4
4
12 24 48 72
0.5 1 1.5 2
Time
Concentration
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000652
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
-60.9
-58.9
-58.6
The SAS System
14:28 Friday, February 19, 2010
difference from .98
------------------------------------ Enzyme=Enzeco Milk=whole -----------------------------------The Mixed Procedure
Fit Statistics
80
BIC (smaller is better)
-58.1
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
195.40
133.68
13.28
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.4999
0.3427
0.1769
0.1175
0.3307
0.1316
0.04755
0.005150
0.1238
0.01370
-0.01210
-0.01990
0.06615
0.001400
-0.00930
-0.01990
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
27.69
18.98
9.80
6.51
18.32
7.29
2.63
0.29
6.86
0.76
-0.67
-1.10
3.66
0.08
-0.52
-1.10
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.0181
0.7791
<.0001
0.4590
0.5123
0.2866
0.0021
0.9391
0.6135
0.2866
81
The SAS System
14:28 Friday, February 19, 2010
difference from .98
------------------------------------- Enzyme=Sigma Milk=raw -------------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Values
4
4
12 24 48 72
0.5 1 1.5 2
Time
Concentration
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000403
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
82
-68.6
-66.6
-66.3
The SAS System
14:28 Friday, February 19, 2010
difference from .98
------------------------------------- Enzyme=Sigma Milk=raw -------------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-65.8
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
436.09
333.80
20.93
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.5852
0.3725
0.2563
0.1492
0.4204
0.1718
0.07965
0.02320
0.2018
0.02480
-0.01265
-0.01990
0.1010
-0.00995
-0.01990
-0.01990
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
41.21
26.23
18.05
10.50
29.61
12.10
5.61
1.63
14.21
1.75
-0.89
-1.40
7.11
-0.70
-1.40
-1.40
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.1218
<.0001
0.0999
0.3862
0.1802
<.0001
0.4935
0.1802
0.1802
83
The SAS System
14:28 Friday, February 19, 2010
difference from .98
------------------------------------- Enzyme=Sigma Milk=skim ------------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Values
4
4
12 24 48 72
0.5 1 1.5 2
Time
Concentration
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000140
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
84
-85.5
-83.5
-83.2
The SAS System
14:28 Friday, February 19, 2010
difference from .98
------------------------------------- Enzyme=Sigma Milk=skim ------------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-82.7
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
1337.92
925.49
62.39
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.6082
0.3734
0.2409
0.1723
0.4017
0.1511
0.07465
0.02510
0.1927
0.01745
-0.01365
-0.01990
0.09020
-0.01075
-0.01990
-0.01990
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
72.72
44.64
28.81
20.60
48.03
18.07
8.93
3.00
23.04
2.09
-1.63
-2.38
10.79
-1.29
-2.38
-2.38
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.0085
<.0001
0.0533
0.1222
0.0301
<.0001
0.2169
0.0301
0.0301
85
The SAS System
14:28 Friday, February 19, 2010
difference from .98
------------------------------------ Enzyme=Sigma Milk=whole ------------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Values
4
4
12 24 48 72
0.5 1 1.5 2
Time
Concentration
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000279
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
86
-74.4
-72.4
-72.1
The SAS System
14:28 Friday, February 19, 2010
difference from .98
------------------------------------ Enzyme=Sigma Milk=whole ------------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-71.7
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
569.37
404.76
28.73
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.5582
0.3534
0.2194
0.1476
0.3703
0.1285
0.04750
0.01505
0.1569
0.006200
-0.01700
-0.01990
0.09495
-0.00745
-0.01990
-0.01990
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
47.23
29.90
18.57
12.49
31.33
10.87
4.02
1.27
13.28
0.52
-1.44
-1.68
8.03
-0.63
-1.68
-1.68
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.0010
0.2210
<.0001
0.6070
0.1696
0.1116
<.0001
0.5373
0.1116
0.1116
87
The SAS System
14:28 Friday, February 19, 2010
difference from .98
------------------------------------ Enzyme=Validase Milk=raw -----------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Time
Concentration
4
4
Values
12 24 48 72
0.25 0.5 0.75 1
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.001208
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
-51.0
-49.0
-48.7
The SAS System
14:28 Friday, February 19, 2010
difference from .98
------------------------------------ Enzyme=Validase Milk=raw -----------------------------------The Mixed Procedure
Fit Statistics
88
BIC (smaller is better)
-48.2
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
96.62
65.68
8.52
<.0001
<.0001
0.0001
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.4934
0.3138
0.1666
0.07965
0.2822
0.05915
0.01835
-0.00890
0.1041
-0.00905
-0.01185
-0.01990
0.05045
-0.01335
-0.01990
-0.01990
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
20.08
12.77
6.78
3.24
11.48
2.41
0.75
-0.36
4.24
-0.37
-0.48
-0.81
2.05
-0.54
-0.81
-0.81
<.0001
<.0001
<.0001
0.0051
<.0001
0.0285
0.4661
0.7220
0.0006
0.7175
0.6362
0.4300
0.0568
0.5945
0.4300
0.4300
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
89
The SAS System
14:28 Friday, February 19, 2010
difference from .98
----------------------------------- Enzyme=Validase Milk=skim -----------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Time
Concentration
4
4
Values
12 24 48 72
0.25 0.5 0.75 1
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.002023
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
90
-42.8
-40.8
-40.5
The SAS System
14:28 Friday, February 19, 2010
difference from .98
----------------------------------- Enzyme=Validase Milk=skim -----------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-40.0
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
85.25
49.53
5.99
<.0001
<.0001
0.0010
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.6017
0.3447
0.2333
0.1120
0.2978
0.1021
0.03420
-0.00230
0.1355
0.003300
-0.01440
-0.01990
0.05485
-0.01990
-0.01990
-0.01990
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
18.92
10.84
7.33
3.52
9.36
3.21
1.08
-0.07
4.26
0.10
-0.45
-0.63
1.72
-0.63
-0.63
-0.63
<.0001
<.0001
<.0001
0.0028
<.0001
0.0054
0.2981
0.9432
0.0006
0.9186
0.6568
0.5403
0.1038
0.5403
0.5403
0.5403
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
91
The SAS System
14:28 Friday, February 19, 2010
difference from .98
----------------------------------- Enzyme=Validase Milk=whole ----------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Time
Concentration
4
4
Values
12 24 48 72
0.25 0.5 0.75 1
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.002475
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
-39.5
-37.5
-37.2
The SAS System
14:28 Friday, February 19, 2010
difference from .98
----------------------------------- Enzyme=Validase Milk=whole ----------------------------------The Mixed Procedure
Fit Statistics
92
BIC (smaller is better)
-36.8
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
24.97
34.38
2.58
<.0001
<.0001
0.0473
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.3565
0.2615
0.1403
0.04455
0.3369
0.1116
0.02890
-0.00650
0.1527
-0.00245
-0.01990
-0.01990
0.08750
-0.00955
-0.01440
-0.01990
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
10.13
7.43
3.99
1.27
9.58
3.17
0.82
-0.18
4.34
-0.07
-0.57
-0.57
2.49
-0.27
-0.41
-0.57
<.0001
<.0001
0.0011
0.2235
<.0001
0.0059
0.4234
0.8557
0.0005
0.9453
0.5794
0.5794
0.0243
0.7895
0.6877
0.5794
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
93
The SAS System
14:28 Friday, February 19, 2010
difference from .99
------------------------------------ Enzyme=Dansico Milk=raw ------------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Time
Concentration
4
4
Values
12 24 48 72
0.25 0.5 0.75 1
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000153
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
-84.0
-82.0
-81.8
The SAS System
14:28 Friday, February 19, 2010
difference from .99
------------------------------------ Enzyme=Dansico Milk=raw ------------------------------------The Mixed Procedure
Fit Statistics
94
BIC (smaller is better)
-81.3
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
554.23
358.67
71.37
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.4595
0.2519
0.1194
0.06315
0.2357
0.08050
0.02945
-0.00090
0.07500
0.005600
-0.00990
-0.00990
0.01470
-0.00990
-0.00990
-0.00990
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
0.008751
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
52.51
28.78
13.64
7.22
26.93
9.20
3.37
-0.10
8.57
0.64
-1.13
-1.13
1.68
-1.13
-1.13
-1.13
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.0039
0.9194
<.0001
0.5313
0.2746
0.2746
0.1124
0.2746
0.2746
0.2746
95
The SAS System
14:28 Friday, February 19, 2010
difference from .99
------------------------------------ Enzyme=Dansico Milk=skim -----------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Time
Concentration
4
4
Values
12 24 48 72
0.25 0.5 0.75 1
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000422
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
-67.8
-65.8
-65.6
The SAS System
14:28 Friday, February 19, 2010
difference from .99
------------------------------------ Enzyme=Dansico Milk=skim -----------------------------------The Mixed Procedure
Fit Statistics
96
BIC (smaller is better)
-65.1
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
263.96
321.14
39.40
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.6126
0.2582
0.1433
0.06560
0.3633
0.1169
0.04730
0.004600
0.1608
0.001300
-0.00990
-0.00990
0.06690
-0.00925
-0.00990
-0.00990
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
0.01452
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
42.19
17.78
9.87
4.52
25.02
8.05
3.26
0.32
11.08
0.09
-0.68
-0.68
4.61
-0.64
-0.68
-0.68
<.0001
<.0001
<.0001
0.0004
<.0001
<.0001
0.0049
0.7555
<.0001
0.9298
0.5051
0.5051
0.0003
0.5331
0.5051
0.5051
97
The SAS System
14:28 Friday, February 19, 2010
difference from .99
----------------------------------- Enzyme=Dansico Milk=whole -----------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Time
Concentration
4
4
Values
12 24 48 72
0.25 0.5 0.75 1
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.001516
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
98
-47.4
-45.4
-45.1
The SAS System
14:28 Friday, February 19, 2010
difference from .99
----------------------------------- Enzyme=Dansico Milk=whole -----------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-44.6
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
41.32
28.32
5.21
<.0001
<.0001
0.0021
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.3996
0.1992
0.1146
0.05785
0.2180
0.09135
0.02175
-0.00100
0.05840
0.006500
-0.00990
-0.00990
0.02000
-0.00185
-0.00585
-0.00990
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
0.02753
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
14.52
7.23
4.16
2.10
7.92
3.32
0.79
-0.04
2.12
0.24
-0.36
-0.36
0.73
-0.07
-0.21
-0.36
<.0001
<.0001
0.0007
0.0518
<.0001
0.0043
0.4410
0.9715
0.0498
0.8163
0.7238
0.7238
0.4780
0.9473
0.8344
0.7238
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
99
The SAS System
14:28 Friday, February 19, 2010
difference from .99
------------------------------------- Enzyme=Enzeco Milk=raw ------------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Values
4
4
12 24 48 72
0.5 1 1.5 2
Time
Concentration
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.001696
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
100
-45.6
-43.6
-43.3
The SAS System
14:28 Friday, February 19, 2010
difference from .99
------------------------------------- Enzyme=Enzeco Milk=raw ------------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-42.8
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
96.09
53.64
4.80
<.0001
<.0001
0.0032
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.5655
0.3519
0.2716
0.1337
0.3297
0.1507
0.1254
0.01810
0.1681
0.02490
0.01035
-0.00990
0.07580
-0.00435
-0.00990
-0.00990
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
0.02912
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
19.42
12.08
9.32
4.59
11.32
5.17
4.31
0.62
5.77
0.86
0.36
-0.34
2.60
-0.15
-0.34
-0.34
<.0001
<.0001
<.0001
0.0003
<.0001
<.0001
0.0005
0.5430
<.0001
0.4052
0.7269
0.7383
0.0192
0.8831
0.7383
0.7383
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
101
The SAS System
14:28 Friday, February 19, 2010
difference from .99
------------------------------------ Enzyme=Enzeco Milk=skim ------------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Values
4
4
12 24 48 72
0.5 1 1.5 2
Time
Concentration
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000803
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
-57.5
-55.5
-55.3
The SAS System
14:28 Friday, February 19, 2010
difference from .99
------------------------------------ Enzyme=Enzeco Milk=skim ------------------------------------The Mixed Procedure
Fit Statistics
102
BIC (smaller is better)
-54.8
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
242.30
163.96
17.73
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.6482
0.3967
0.2567
0.1331
0.3974
0.1207
0.06475
0.01725
0.1757
0.02135
0.000450
-0.00990
0.07595
-0.00845
-0.00990
-0.00990
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
0.02004
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
32.35
19.79
12.81
6.64
19.83
6.03
3.23
0.86
8.77
1.07
0.02
-0.49
3.79
-0.42
-0.49
-0.49
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.0052
0.4020
<.0001
0.3025
0.9824
0.6280
0.0016
0.6789
0.6280
0.6280
103
The SAS System
14:28 Friday, February 19, 2010
difference from .99
------------------------------------ Enzyme=Enzeco Milk=whole -----------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Values
4
4
12 24 48 72
0.5 1 1.5 2
Time
Concentration
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000652
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
104
-60.9
-58.9
-58.6
The SAS System
14:28 Friday, February 19, 2010
difference from .99
------------------------------------ Enzyme=Enzeco Milk=whole -----------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-58.1
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
195.40
133.68
13.28
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.5099
0.3527
0.1869
0.1276
0.3407
0.1416
0.05755
0.01515
0.1338
0.02370
-0.00210
-0.00990
0.07615
0.01140
0.000700
-0.00990
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
0.01805
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
28.24
19.53
10.35
7.07
18.87
7.84
3.19
0.84
7.41
1.31
-0.12
-0.55
4.22
0.63
0.04
-0.55
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.0057
0.4137
<.0001
0.2078
0.9088
0.5910
0.0007
0.5367
0.9696
0.5910
105
The SAS System
14:28 Friday, February 19, 2010
difference from .99
------------------------------------- Enzyme=Sigma Milk=raw -------------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Values
4
4
12 24 48 72
0.5 1 1.5 2
Time
Concentration
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000403
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
106
-68.6
-66.6
-66.3
The SAS System
14:28 Friday, February 19, 2010
difference from .99
------------------------------------- Enzyme=Sigma Milk=raw -------------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-65.8
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
436.09
333.80
20.93
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.5952
0.3825
0.2663
0.1592
0.4304
0.1818
0.08965
0.03320
0.2118
0.03480
-0.00265
-0.00990
0.1110
0.000050
-0.00990
-0.00990
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
0.01420
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
41.92
26.94
18.75
11.21
30.31
12.80
6.31
2.34
14.91
2.45
-0.19
-0.70
7.82
0.00
-0.70
-0.70
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.0327
<.0001
0.0261
0.8543
0.4957
<.0001
0.9972
0.4957
0.4957
107
The SAS System
14:28 Friday, February 19, 2010
difference from .99
------------------------------------- Enzyme=Sigma Milk=skim ------------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Values
4
4
12 24 48 72
0.5 1 1.5 2
Time
Concentration
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000140
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
108
-85.5
-83.5
-83.2
The SAS System
14:28 Friday, February 19, 2010
difference from .99
------------------------------------- Enzyme=Sigma Milk=skim ------------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-82.7
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
1337.92
925.49
62.39
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.6182
0.3834
0.2509
0.1823
0.4117
0.1611
0.08465
0.03510
0.2027
0.02745
-0.00365
-0.00990
0.1002
-0.00075
-0.00990
-0.00990
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
0.008363
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
73.92
45.84
30.00
21.79
49.22
19.26
10.12
4.20
24.23
3.28
-0.44
-1.18
11.98
-0.09
-1.18
-1.18
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.0007
<.0001
0.0047
0.6683
0.2538
<.0001
0.9297
0.2538
0.2538
109
The SAS System
14:28 Friday, February 19, 2010
difference from .99
------------------------------------ Enzyme=Sigma Milk=whole ------------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Values
4
4
12 24 48 72
0.5 1 1.5 2
Time
Concentration
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.000279
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
110
-74.4
-72.4
-72.1
The SAS System
14:28 Friday, February 19, 2010
difference from .99
------------------------------------ Enzyme=Sigma Milk=whole ------------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-71.7
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
569.37
404.76
28.73
<.0001
<.0001
<.0001
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
0.5
1
1.5
2
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.5682
0.3634
0.2295
0.1575
0.3803
0.1385
0.05750
0.02505
0.1669
0.01620
-0.00700
-0.00990
0.1049
0.002550
-0.00990
-0.00990
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
0.01182
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
48.08
30.75
19.42
13.33
32.18
11.72
4.87
2.12
14.12
1.37
-0.59
-0.84
8.88
0.22
-0.84
-0.84
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.0002
0.0500
<.0001
0.1894
0.5619
0.4145
<.0001
0.8319
0.4145
0.4145
111
The SAS System
14:28 Friday, February 19, 2010
difference from .99
------------------------------------ Enzyme=Validase Milk=raw -----------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Time
Concentration
4
4
Values
12 24 48 72
0.25 0.5 0.75 1
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.001208
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
-51.0
-49.0
-48.7
The SAS System
14:28 Friday, February 19, 2010
difference from .99
------------------------------------ Enzyme=Validase Milk=raw -----------------------------------The Mixed Procedure
Fit Statistics
112
BIC (smaller is better)
-48.2
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
96.62
65.68
8.52
<.0001
<.0001
0.0001
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.5034
0.3238
0.1766
0.08965
0.2922
0.06915
0.02835
0.001100
0.1141
0.000950
-0.00185
-0.00990
0.06045
-0.00335
-0.00990
-0.00990
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
0.02458
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
20.48
13.17
7.18
3.65
11.89
2.81
1.15
0.04
4.64
0.04
-0.08
-0.40
2.46
-0.14
-0.40
-0.40
<.0001
<.0001
<.0001
0.0022
<.0001
0.0125
0.2656
0.9649
0.0003
0.9696
0.9409
0.6924
0.0257
0.8933
0.6924
0.6924
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
113
The SAS System
14:28 Friday, February 19, 2010
difference from .99
----------------------------------- Enzyme=Validase Milk=skim -----------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Time
Concentration
4
4
Values
12 24 48 72
0.25 0.5 0.75 1
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.002023
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
114
-42.8
-40.8
-40.5
The SAS System
14:28 Friday, February 19, 2010
difference from .99
----------------------------------- Enzyme=Validase Milk=skim -----------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-40.0
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
85.25
49.53
5.99
<.0001
<.0001
0.0010
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.6117
0.3547
0.2433
0.1220
0.3078
0.1121
0.04420
0.007700
0.1455
0.01330
-0.00440
-0.00990
0.06485
-0.00990
-0.00990
-0.00990
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
0.03180
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
19.23
11.15
7.65
3.84
9.68
3.53
1.39
0.24
4.58
0.42
-0.14
-0.31
2.04
-0.31
-0.31
-0.31
<.0001
<.0001
<.0001
0.0015
<.0001
0.0028
0.1836
0.8118
0.0003
0.6813
0.8917
0.7596
0.0583
0.7596
0.7596
0.7596
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
115
The SAS System
14:28 Friday, February 19, 2010
difference from .99
----------------------------------- Enzyme=Validase Milk=whole ----------------------------------The Mixed Procedure
Model Information
Data Set
Dependent Variable
Covariance Structure
Estimation Method
Residual Variance Method
Fixed Effects SE Method
Degrees of Freedom Method
WORK.GOOD
zeroed
Diagonal
REML
Profile
Model-Based
Residual
Class Level Information
Class
Levels
Time
Concentration
4
4
Values
12 24 48 72
0.25 0.5 0.75 1
Dimensions
Covariance Parameters
Columns in X
Columns in Z
Subjects
Max Obs Per Subject
1
25
0
1
32
Number of Observations
Number of Observations Read
Number of Observations Used
Number of Observations Not Used
32
32
0
Covariance Parameter
Estimates
Cov Parm
Estimate
Residual
0.002475
Fit Statistics
-2 Res Log Likelihood
AIC (smaller is better)
AICC (smaller is better)
116
-39.5
-37.5
-37.2
The SAS System
14:28 Friday, February 19, 2010
difference from .99
----------------------------------- Enzyme=Validase Milk=whole ----------------------------------The Mixed Procedure
Fit Statistics
BIC (smaller is better)
-36.8
Type 3 Tests of Fixed Effects
Effect
Time
Concentration
Time*Concentration
Num
DF
Den
DF
F Value
Pr > F
3
3
9
16
16
16
24.97
34.38
2.58
<.0001
<.0001
0.0473
Standard
Estimate
Error
DF
t Value
Pr > |t|
0.3665
0.2715
0.1504
0.05455
0.3469
0.1217
0.03890
0.003500
0.1628
0.007550
-0.00990
-0.00990
0.09750
0.000450
-0.00440
-0.00990
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
0.03518
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
10.42
7.72
4.27
1.55
9.86
3.46
1.11
0.10
4.63
0.21
-0.28
-0.28
2.77
0.01
-0.13
-0.28
<.0001
<.0001
0.0006
0.1405
<.0001
0.0032
0.2851
0.9220
0.0003
0.8328
0.7820
0.7820
0.0136
0.9900
0.9020
0.7820
Least Squares Means
Effect
Time
Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
Time*Concentration
12
12
12
12
24
24
24
24
48
48
48
48
72
72
72
72
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
0.25
0.5
0.75
1
117