A tool for analyzing multivariate data that has been especially appropriate
for theory testing (Bagozzi, 1980; Steenkamp and Baumgartner, 2000).
* Latent variables can not be observed directly (Chin, Peterson &
Brown, 2008) * Path Analysis: is a special case of SEM that only
involves observed (manifest) variables (Savalei & Bentler, 2010).
SEMs go beyond ordinary regression models to incorporate multiple
independent and dependent variables as well as hypothetical latent constructs
which may cluster several observed variables (Savalei & Bentler, 2010).
SEM have become ubiquitous in all the social and
behavioral sciences (e.g., MacCallum & Austin, 2000).
Anderson and Gerbin (1988) conducted a review and
recommended a 2 step approach: 1) A confirmatory
measurement, or factor analysis, model specifies the relations
of the observed measures to their posited underlying
constructs, with the constructs allowed to intercorrelate freely.
2) A confirmatory structural model then specifies the causal
relations of the constructs to one another.
Baumgartner and Homburg (1996) conducted a review of
use of SEM in marketing research.
Modeling Process (Savalei &
1) Model specification: Specify variables and constructs
2) Model estimation: Iterative process to stimate parameters
3) Model evaluation: There are two components to model fit: statistical fit and
practical fit. Statistical fit is evaluated via a formal test of the hypothesis ( T).
Practical fit is evaluated by examining various indices of fit: standardized root
mean-square residual (SRMR) <.05. Goodness of Fit index (GFI) related to R2 in
ordinary regression. AGFI (Adjusted GFI), is analogous to the adjusted R2 . Both
GFI and AGFI take on values between 0 and 1, with values less than 0.90 often
considered unacceptable. Comparative Fit Index (CFI) with values between 0
and 1. Preferable close to 0.
4) Model modification : if the proposed model dont fit the data
5) Parameter Testing: To interpret parameter estimates and to test for
their statistical significance. Several tests used, in particular z-tests, Wald
tests, and chi-square difference tests.
Rules of Thumb
Bentler & Bonett, 1980: at least three items per construct.
Bentler & Chau, 1987: Sample size of 5 to 10 subjects
per item and up to 300
Baumgartner, 1996: Minimum 3 or 4 indicators per latent
variable, large sample sizes 5:1, assumption of normality,
model should be identified
Fornell & Larcker (1981): Standardized loading estimates
should be .5 or higher, ideally .7 or higher. Average of
variance Extracted (AVE) should be .5 or higher. Construct
Reliability (CR) should be .7 or higher, between .6 and .7 is
The relationship between a manifest variable and a construct is expressed as being either
formative or reflective. If the relationship is formative, the manifest variable (indicator) cause
the construct, whereas if the relationship is reflective, the construct cause the manifest
variable (Jarvis, Mckenzie, & podsakoff, 2003). Most structural equation models specify the
manifest variable–construct relationship as reflective (Chin, Peterson & Brown, 2008)