Page 103 - Contributed Paper Session (CPS) - Volume 8

CPS2205 Abdul Aziz A. Rahaman et al.
Likert-scale form and rated as: Strongly Disagree=1, Disagree=2, Not sure=3,
Agree=4 and Strongly Agree=5.

2.2 Model Specification, Estimations and Tests
2.2.1 Structural Equation Modelling versus Ordinal Logistic Regression
The four steps of SEM, specification, identification, estimation, and model
evaluation, are examined and an example is introduced to clarify these
concepts. In addition, model diagnostics that have been developed under the
SEM framework are briefly discussed which can be viewed as part of model
evaluation. However, in considering methods for Likert scale responses having
more than two possible options, a number of methods have been developed
for handling the various possibilities. The most appropriate method developed
for this case is the ordinal logit concept (Agresti, 2002).

2.2.2 Latent Variable Model for Structural Equation
From the Fig. 1 below, considering the SEM framework, latent variables are
considered to either be exogenous, such as  , as their causes lie outside the
1
model, or endogenous, like η1 and η2, as their causes lie within the model. In
Figure 1, it is hypothesized that  is a cause of both η1 and η2 and that η1 is a
1
cause of η2. The latent variable model for the hypothetical model in Figure 1
can be written in equation form as:
=  +  (1)
11 1
1
1
= +  +  (2)
1
21 1
21 2
2
The random errors  and  are assumed to have an expected value of zero
2
1
and homoskedastic variances and uncorrelated with  . Thus (1) and (2) can
1
be written more compactly as
= +  +  (3)

2.2.3 Measurement Model for Structural Equation
The measurement model links the latent variables with observed variables
(the terms observed variables, indicators, measures, and manifest variables are
used interchangeably). The example in Figure 1 posits that each latent variable
has three indicators, each of which is associated with only one factor. The
indicators for 1 are y1 , y2 and y3 , the indicators for 2 are y4 , y5 and y6 , and
the indicators for 1 are x1 , x2 , x3 , x4 and x5 . The measurement model
associated with Figure 1 is written more compactly in matrix notation as:
= Λ  +  (4)

= Λ + (5)

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