Discriminant Analysis Model for Predicting Contractor Performance in Hong
Kong
By: C.M.Tam, Dept. of Building & Construction, City Polytechnic of Hong Kong
F.C.Harris, School of Construction, Wolverhampton Polytechnic, England
1. Introduction to the Problem
2, score
Construction clients commonly try to gauge a contractor's potential performance on a past record of
finishing on time, to cost and with good quality of
work before inviting bids. However, the tendering
method can only measure a portion of the cost component as contractors often succeed in obtaining
claims for extras. Unfortunately, the other two components, time (completion on time) and quality of work,
are even more difficult to assess at the tendering
Stage. While careful pre-selection may help in judgement, decision making is subjective and often not
accurate.
Other methods need to be devised to include as much
quantitative and objective factors as possible in
assessing the contractor performance. This aspects
form the basis of the research described in this paper
where a quantitative model has been developed.
=
C, + C, V, + C, V, + ... CoVn
Where:
2,score is the contractor perfromance index which is a
value describing the contractors' performance on a
scale between good to bad.
Ci are the coefficients which produce the desired
characteristics in the function.
V, are the variables in the function which govern the
contractors' performance.
In order to derive the function, the authors have spent
one and a half year to coiiect data of thirty-one
completed projects through interviewing ciients and
contractors and these views are being used to separate
the samples into two groups- good and bad.
The types of project included in this research are as
follows:
2. Determination of Contractor Performance
Contract sum
Number of proiects
The mathematical technique of Discriminant Analysis
was adopted in the research to evaluate the performance of contractors.
Below HK!§ 1million
1
HK!§ 1to 5 million
4
Above HK$5 to 50 million
9
Above H a 5 0 to 100 million
9
Above HK$100 million
11
Total :
34
The number of contractors involved are fourteen.
Their size rmges from having 12 number of staff to
1000.
Discriminant analysis is a procedure used to classify
an object into one of several a priori groupings
dependent upon the individual characteristics of the
object. After the groups are established, data are
collected for the objects in the groups. The discriminant analysis then attempts to derive a linear combination of these characteristics which best discriminates between the groups. If a particular object, for
instance a contractor or a project, has characteristics
which can be quantified, the discriminant analysis
determines a Set of discriminant coefficients. The
discriminant analysis technique has the advantage of
considering an entire profile of characteristics of a
project or a contractor, as weii as the interaction of
these properties.'
3. The Attributes of Contractors included in the Z,
Model
By applying the discriminant analysis technique in this
research, it is hoped that the discriminant function of
the following form is developed to transform individual properties of construction projects to a Single
discriminant score or Z value which is then used to
classify the performance behaviour:
Discriminant analysis then helps in analysing the
differentes between the groups and/or providcs a
means to assign (classify) any case into the group
which it most closely resembles3 The most difficult
part of this procedure is to sort out precisely the
factors which can delineate the difference in contrac-
The main task centres on ascertaining the attributes of
contractors and the variables influencing performance
based on the premise that two or more groups exist
which are presumed to differ according to the degree
of these attributes measured in terms of the variables.
tors' performance. At this Stage, it is better to include
as many attributes as possible as long as they are
obtainable and considered as attributable to the
performance behaviour. The model will remove those
attributes which are not significant.
4.2
Comparing the significance of variables and
eliminating unnecessary variables.
4.3
Testing the formula's and the coefficient's lcvel
of significance.
4.4
Calculating the discriminant Score for the tcst
samples.
The factors included to date are as fo1lows:Interna1 Factors:
Staff training programme*
Plant ownership policy'
Size of the company*
Quality of management team - Percentage of
professionaily qualified staff
Quality of management team - Project leader's
experience*
Past performance of the project manager*
Contractor's experience in the type of job*
Contractor's work load'
Contractor's past performance or image'
Number of years in the business*
Origin of the company*
Amount of directly employed labour*
Listed on the stock market*
Decision making centralised in head office or
de-centralised to site*
Contractor is client's subsidiary firm*
External Factors:
The above are all internal attributes of contractors,
however, there may be many external influences which
affect a contractor's performance such as:
3.16
3.17
3.18
3.19
3.20
The Architect' performance'
Architect's or client's supervision and control
on the quality of work and work progress*
Punctuality of payment by the client*
Complexity of the project*
Profitability of the project'
(Owing to the limitation of space, the ways to quantdy
the variables are not described here. For those who
are interested in them, please refer to the authors.)
4. Statistical Packa~eUsed
As mentioned at the beginning, discriminant analysis
provides a potentially useful technique for the purpose
but requires considerable calculation. Hence, a
computer Software package was selected to aid the
process and SPSS(")PCwas chosen and appears to be
quite adequate in performing the following tasks:
4.1
Estimating coefficients and derives the function.
5. Results
By applying the discriminant analysis technique, the
formula for 2, turns out as fo1lows:Discriminant function = -2.116197 - 0.4960918(COMPLEX) + 12.85458(PROF-STA) +
0.09186742(LEAD-EX) 1.730167(PAST-PER) +
0.9040884(ORIGIN) +
l.l05466(CONTROL)
where
COMPLEX: The complexity of the project
PROF-STA: The percentage of professionally
qualified staff
LEAD-EX : Project leader's experience
PAST-PER: Contractor's past performance or image
ORIGIN : Origin of the company
CONTROL : Architect's or client's supervision and
control on the quality of work and work
progress
Table 1 Unstandardized Canonical Discriminant
Function Coefficients
I
COMPLEX
PROF-STA
LEAD-EX
PAST-PER
ORIGIN
CONTROL
(constant)
Table 2 Standardized Canonical Discriminant Function Coefficients
~ M P L E X
PROF-STA
LEAD-EX
PAST-PER
ORIGIN
{CONTROL
-0.79039>
1.01346
0.63551
- 1.09492
0.57734
0.92512 I
The unstandardized coefficients are the multipliers of
are shared and the individual coefficients are not
meaningful.
the variables when they are expressed in the original
units. The standardized coefficients are standardized
to a mean of 0 and a standard deviation of 1.
There are some variables which were eliminated in
the model but which were expected to fall into the
group, like the profitability of the project since most
contractors interviewed expressed the importance of
this variable in their performance motivation. This
may be due to the inaccuracy of the pre-tender
estimate (the variable was guaged by the tender price
over the pre.-tender estimate).
Since the variables are correlated, it is not possible to
assess the importance of an individual variable. The
value of the coefficient for a particular variable
depends on the other variables included in the function.
Sometimes, it is tempting to interpret the magnitudes
of the coefficients as indicators of the relative importance of variables because variables with large coefficients are thought to contribute more to the overall
discriminant function. The magnitude of unstandardized coefficients, however is not a good indicator of
the relative importance since the variables have
different units in which they are measured.)
Other variables were removed because the model has
considered them not signifcant in the F statistics
calculation3..
5.1 Ouality of classification
Fig. 1shows the frequency distribution against the
discriminant Scores of the two groups.
From the standardized coefficients, it is noted that the
past performance has the highest magnitude and the
rest in descending order of importance are the quality
of staff- percentage of professionally quality staff,
architect's or client's supervision and control on the
Progress and quality of work, the complexity of the
project, the project leader's working experience and
the origin of the company (refer to table 2).
The classification result can be summarised as follows:
Another way to assess the contribution of a variable to
the discriminant function is to examine the correlations between the values of the function and the values
of the variables. The computation of the coefficients is straight forward. For each case the value
of discriminant function is computed, and the
Pearson correlation coefficients between it and the
original variables are obtained?
Actual group
No. of
cases
Group 1
23
Sroup 2
8
Figure
Predicted group
membership
1
2
23
0
(100%) (0%)
0
(0%)
8
(100%)
Frequency Distribution Histograrn
a g h t Discriminant Scores for Good and Bad groups
Table 3 The pool within m o u ~ correlations
s
between discriminatin~variables and canonical
discriminant functions are:/AST-PER
ORIGIN
CONTROL
PROF-STA
COMPLEX
tEAD-EX
-0.45313
0.37160
0.34601
-0.14815
-0.1428
0.00592J
In comparing the orders in table 2 and 3, it will be
noticed that PROF-STA has the second highest
contribution in table 2 and carries a positive sign
while in table 3, it falls to fourth and has a negative
sign. The order of contribution of ORIGIN in table 2
ranks the last but second in the table 3. This occurs
because PROF-STA has a very high correlation with
the ORIGIN (correlation coefficients of 0.69184).
Thus the contribution of PROF-STA and ORIGIN
-6
-4
-2
0
2
4
6
Z Score
Percentage of "grouped" cases correctly classified is
100%. The canonical correlation is 0.8671 and the
~ i g ~ c a n ciseless
. than 0.00005 when using chi-squarc
to test the model.
5.2 Variables shortlisted in the model:
the company size and control which are 0.53326 and
0.59469 respectively.
5.2.1 Past ~erformanceof contractor:
5 3 Conclusion
From the model, it can be noted that the past performance of the contractor ascribes their future
performance very much. This reflects some of the top
management's hard attitude in managing projects
cause they tried to maxirnise the profit in every project
irrespective of the relationship with the clients. Some
contractors stand very firm in the position of claims.
Some may have hired claims consultants at the outset
of the contract. These may upset the ciients.
The purpose of this paper was to investigate empirically the characteristics of contractor performance
behaviour and attempt to develop an accurate Performance prediction model. Discriminant analysis was
used to accompiish this with the intrinsic characteristics of contractors and the external influence by thc
architects and the clients serving as predictive variables.
5 2 2 Ori~inof the company
Local Chinese contractors have their own way of
running business. They would prefer commercial
settlements rather than bringing the case to arbitration or court in order to maintain a good relationship
with the ciients.
Most overseas contractors in Hong Kong (especially
those from the Western countries) are very claim
conscious. Further they may have difficulties in
managing local subcontractors; particularly the labour
only subcontractors. (Japanese contractors are deliberately excluded from this catagory as they do not care
about claims in order to 'please' the clients.)
5 2 3 Architect's or client's sunervision and control
Early signalling of the client's dissatisfaction on the
work Progress and the quality of works by issuing
architectual instructions and warnings can reduce
disputes at the end of the contract.
By observing the variables shortlisted in the model,
the analysts concluded that there were differences in
them of good performance compared to bad. The
model contained six variables which serve as the
predictive variables. These variables have been
explored in section five.
Results of the study indicate that it is possible to
classdy contractors into either having good or bad
performance using the variables included in the
model.
6. Further Research Work
The authors will carry out tests on an independent
sample of projects to verify the reliability of the
model. Furthermore, investigation of models for
independent 2, Scores based separately on cost, time
and quality will be studied.
References:
5.2.4 Qualitv of mana~ementteam- ~ e r c e n t a ~ofe
professionally aualified staff and proiect leader's
l.'"The Prediction of Corporate Bankruptcy- a Discriminant Analysis" Garland Publishing, Inc. by
Edward IJUtman
Both of these have an impact on the contractor
performance since they measure part, although not all,
of the management team's quality.
2. "Discriminant Analysis" SAGE Publication by
Williarn R.Klecka.
3. "SPSS User Manual"
5 2 5 Com~lexitvof the proiect
The degree of importance of this variable may be
suppressed in the way that clients may choose large
and weli established contractors for the compiicated
and large jobs while keeping the simple and smaii jobs
to the smali and young contractors and thus the data
coiiected is biased. Further, the architect's or the
client's supervision on complicated jobs would be
tighter. These can be revealed from the relatively high
correlation between the variables of complexity and
4. "Predicting company failure in the construction
industry" by RJ.Mason and F.C.Harris, Proc. Instn
Civ. Engrs, Part I 1979, May.