6.4 Modelling strategy
The two-step SEM modelling procedure described by Anderson and Gerbing
(1988) firstly (during Step 1) establishes a confirmatory factor analysis (CFA)
measurement model in which:
(a) the relationships between the observed variables (also referred to as items, or
indicators) and the latent factors are specified (according to theory or previous
empirical research findings); and
(b) all of the latent factors are allowed to intercorellate freely (indicated with bi-
directional connecting arrows that specify a non-causal correlation).
Where each observed variable (indicator) is linked only to one latent factor, the
CFA is described as being unidimensional or congeneric. In multidimensional
CFAs, indicators can have loadings on two or more latent factors. In practice, it is
more usual for CFAs to be specified in unidimensional formats since this allows for
more exact estimates of convergent and discriminant validity to be made (Kline
2005: 167 - 168). Convergent and discriminant validity are both aspects of
construct validity and will be discussed in greater depth below.
Step 2 of Anderson and Gerbing’s two-step approach proceeds when a
measurement model with satisfactory fit has been established. Step 2 involves
respecifying the model by replacing, as dictated by the theory to be tested, the
bi-directional (non-causal) arrows with uni-directional arrows indicating causal
relations between latent factors. Independent latent factor variables (also refered
to as exogenous factors in SEM analyses while dependent variables are referred to
as endogenous variables) may still (but not neccesarily) covary in a non-causal
manner as specified by the theory to be tested and some connections between
factors may be dropped altogether (indicating no hypothesised relationship
between these variables).
Within the Model Generating (MG) approach to structural equation modelling it is
possible to modify – or respecify - the measurement and structural models in
such a way that model fit is improved. During Step 1 this is often achieved by
removing poorly performing indicators (observed variables) based on the
statistical feasibility of parameter estimates (the strength and statistical
significance of indicators’ respective factor loadings) in combination with an
assessment of the appropriateness of indicators’ standard errors (Byrne 2010: