LISREL is defined by a hypothesized
pattern of linear relationships among a set of
measured and latent variables.
Such a pattern of linear relationships can be
represented mathematically in a variety of
There exist alternative ways of organizing
variables and defining parameter matrices,
which yield alternative mathematical
frameworks for representing data models
and covariance structure models.
Principle Component Analysis
component analysis (PCA) is a
mathematical procedure uses orthogonal
transformation to convert a set of observations
of possibly correlated variables into a set of
values of linearly uncorrelated variables
called principal components.
The number of principal components is less than
or equal to the number of original variables.
Principal components are guaranteed to be
independent if the data set is jointly normally
PCA is sensitive to the relative scaling of the
Variance analysis shows that the
“Layout” variable having the most impact
on “Repurchase Link” in PC3 i.e. 0.722.
Structural Equation Model
equation modeling (SEM) is
a statistical technique for testing and estimating causal
relations using a combination of statistical data and
qualitative causal assumptions.
This definition of SEM was articulated by the
geneticist Sewall Wright (1921), the
economist Trygve Haavelmo (1943) and the cognitive
scientist Herbert A. Simon(1953), and formally
defined by Judea Pearl (2000) using a calculus of
Structural equation models (SEM) allow both
confirmatory and exploratory modeling, meaning they
are suited to both theory testing and theory
Structural Equation Model
concepts used in the model must
then be operationalized to allow testing
of the relationships between the concepts
in the model.
The model is tested against the obtained
measurement data to determine how well
the model fits the data.
The causal assumptions embedded in the
model often have falsifiable implications
which can be tested against the data.
(Goodness of Fit Index)
NFI(Normed Fit Index)
CFI (Comparative Fit Index)
Goodness of Fit Index
goodness of fit index (GFI) is a
measure of fit between the hypothesized
model and the observed covariance
matrix. The GFI ranges between 0 and 1,
with a cutoff value of .9 generally
indicating acceptable model fit.
Normed Fit Index
normed fit index (NFI) analyzes the
discrepancy between the chi-squared
value of the hypothesized model and the
chi-squared value of the null model.
However, this NFI was found to be very
susceptible to sample size. Value for the
NFI should range between 0 and 1, with a
cutoff of .95 or greater indicating a good
Comparative Fit Index
comparative fit index (CFI) analyzes the
model fit by examining the discrepancy
between the data and the hypothesized
model, while adjusting for the issues of
sample size inherent in the chi-squared test
of model fit, and the normed fit index. CFI
values range from 0 to 1, with larger values
indicating better fit; a CFI value of .90 or
larger is generally considered to indicate
acceptable model fit.