Conducting a Path Analysis with SAS Proc Calis
We shall use the data from the thesis published in this article:
Ingram, K. L., Cope, J. G., Harju, B. L., & Wuensch, K. L. (2000). Applying to graduate school: A test
of the theory of planned behavior. Journal of Social Behavior and Personality, 15, 215-226.
The path model is:
Copy and paste the program boxed below into the SAS editor and then run it.
options formdlim='-' nodate pagno=min;
TITLE 'Path Analysis, Ingram Data' ;
data Ingram(type=corr);
INPUT _TYPE_ $ _NAME_ $ Attitude SubNorm PBC Intent Behavior;
CARDS;
N . 60 60 60 60 60
MEAN . 32.02 45.71 40.25 16.92 43.92
STD . 6.96 12.32 7.62 3.83 16.66
CORR Attitude 1 .472 .665 .767 .525
CORR Subnorm
.472 1 .505 .411 .379
CORR PBC
.665 .505 1 .458 .496
CORR Intent
.767 .411 .458 1 .503
CORR Behavior .525 .379 .496 .503 1
Proc Calis PRINT;
LINEQS
Intent = b1 Attitude + b2 SubNorm + b3 PBC + E1,
Behavior = b4 Intent + b5 PBC + E2;
STD E1-E2 = V1-V2;
run;
Explanation of the program.
Rather than input the raw data, I have used correlation matrix input.
The PRINT option in Proc Calis adds to the default output the total effects matrix (and some
other things). To learn more about what the output options are for Proc Calis, click the help icon in
SAS, select the “Index” tab, enter keyword “calis,” and click “Display.” Click “Syntax” and then “Proc
Calis.” On the command bar, click “Edit,” “Find in this topic.” Enter “Displayed Output Options” and
click “Next” twice.
Following the LINEQS statement the model is defined. The first equation indicates that Intent
has paths to it from Attitude, SubNorm, PBC, and E1 (the error term); b1, b2, and b3 are the path
coefficients that we want SAS to estimate for us.
The second equation indicates that Behavior has paths to it from Intent, PBC, and E2. SAS
assumes that the exogenous variables (Attitude, SubNorm, and PBC) are correlated.
The STD statement asks that the error terms be estimated as parameters V1 and V2.
The Output
The Standardized Path Coefficients
Standardized Results for Linear Equations
Intent
=
Behavior =
0.8061 * Attitude + 0.0939 * SubNorm + -0.1255 * PBC + 1.0000
0.3491 * Intent
+ 0.3361 * PBC
+ 1.0000
E2
The Standardized Error Coefficients
Standardized Results for Variances of Exogenous Variables
Variable
Standard
Type
Variable Parameter Estimate
Error
Error
t Value
E1
V1
0.40058
0.08075 4.96056
E2
V2
0.65770
0.10019 6.56441
Standardized Coefficients Among Exogenous Variables
Standardized Results for Covariances Among Exogenous Variables
Estimate
Standard
Error
t Value
_Add4
0.47200
0.10118
4.66473
Attitude
_Add5
0.66500
0.07262
9.15775
SubNorm
_Add6
0.50500
0.09699
5.20686
Var1
Var2
Parameter
SubNorm
Attitude
PBC
PBC
E1
Standardized Direct, Indirect, and Total Effects
Standardized Direct Effects
Effect / Std Error / t Value / p Value
Intent Attitude
Behavior
PBC SubNorm
0.3491
0.1137
3.0693
0.002145
0
0.3361
0.1142
2.9445
0.003234
0
0
0.8061
0.0919
8.7690
<.0001
-0.1255
0.1153
-1.0886
0.2763
0.0939
0.0977
0.9609
0.3366
Intent
Standardized Indirect Effects
Effect / Std Error / t Value / p Value
Intent
Behavior
Attitude
0
PBC SubNorm
0.2814 -0.0438
0.0992 0.0429
2.8364 -1.0199
0.004563 0.3078
0.0328
0.0357
0.9168
0.3592
Standardized Total Effects
Effect / Std Error / t Value / p Value
Intent
Behavior
Intent
Attitude
0.3491
0.2814
0.1137
0.0992
3.0693
2.8364
0.002145 0.004563
0
PBC SubNorm
0.2923
0.1289
2.2679
0.0233
0.0328
0.0357
0.9168
0.3592
0.8061 -0.1255
0.0919 0.1153
8.7690 -1.0886
<.0001 0.2763
0.0939
0.0977
0.9609
0.3366
Measures of Goodness of Fit
A good fitting model is one that can reproduce the original variance-covariance matrix (or
correlation matrix) from the path coefficients, in much the same way that a good factor analytic
solution can reproduce the original correlation matrix with little error.
Absolute Indices. These indices are measures of badness of fit – that is, the larger the index,
the worse the fit.
Fit Summary
Chi-Square
Chi-Square DF
0.8564
2
Pr > Chi-Square 0.6517
This Chi-square tests the null hypothesis that the overidentified (reduced) model fits the data
just as well as does a just-identified (full, saturated) model. In a just-identified model there is a direct
path (not through an intervening variable) from each variable to each other variable. In such a model
the Chi-square will always have a value of zero, since the fit will always be perfect. When you delete
one or more of the paths you obtain an overidentified model and the value of the Chi-square will rise
(unless the path(s) deleted have coefficients of exactly zero). For any model, elimination of any
(nonzero) path will reduce the fit of model to data, increasing the value of this Chi-square, but if the fit
is reduced by only a small amount, you will have a better model in the sense of it being less complex
and explaining the covariances almost as well as the more complex model.
The nonsignificant Chi-square here indicates that the fit between our overidentified model and
the data is not significantly worse than the fit between the just-identified model and the data. While
one might argue that nonsignificance of this Chi-square indicates that the reduced model fits the data
well, even a well-fitting reduced model will be significantly different from the full model if sample size
is sufficiently large.
Standardized RMSR (SRMSR) 0.0191
The smaller the better. A value of 0 indicates perfect fit. Less than .08 is considered good.
RMSEA Estimate
0.0000
RMSEA Lower 90% Confidence Limit 0.0000
RMSEA Upper 90% Confidence Limit 0.2011
Below .01 is excellent, ,05 is good, .10 is mediocre, and above .10 is poor. The confidence
interval gives you an idea of the amount of error in estimating this parameter from your sample data.
Probability of Close Fit 0.6905
This is the p value testing the null hypothesis that the population RMSEA is .05 or less (good).
If p > .05, you conclude that the fit is good.
Incremental Indices. These compare your model to an independence model (a model where
all of the path coefficients are zero). The bigger the better.
Bentler Comparative Fit Index 1.0000
A value below .9 is considered poor, .9 is considered marginal, .95 is good.
Bentler-Bonett Normed Fit Index 0.9936
A value below .9 is considered poor, .9 is considered marginal, .95 is good.
Bentler-Bonett Non-normed Index 1.0461
A value below .9 is considered poor, .9 is considered marginal, .95 is good. If the value
exceeds one, reduce it to one.
Links



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Wuensch’s Stats Lessons
An Introduction to Path Analysis
Adventures in Path Analysis
David Kenney on Fit Indices
Karl L. Wuensch
Dept. of Psychology, East Carolina University, Greenville, NC 27858 USA
April, 2016