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Example
16
Sörbom’s Alternative to
Analysis of Covariance
Introduction
This example demonstrates latent structural equation modeling with longitudinal
observations in two or more groups, models that generalize traditional analysis of
covariance techniques by incorporating latent variables and autocorrelated residuals
(compare to Sörbom, 1978), and how assumptions employed in traditional analysis of
covariance can be tested.
Assumptions
Example 9 demonstrated an alternative to conventional analysis of covariance that
works even with unreliable covariates. Unfortunately, analysis of covariance also
depends on other assumptions besides the assumption of perfectly reliable covariates,
and the method of Example 9 also depends on those. Sörbom (1978) developed a
more general approach that allows testing many of those assumptions and relaxing
some of them.
The present example uses the same data that Sörbom used to introduce his method.
The exposition closely follows Sörbom’s.