The multiple samples approach is one way to look
at latent interaction effects. In this case, the sample is divided
into sub-samples with different parameter values (e.g., low /
high), then a model is calculated for each sub-sample, and then
the parameter estimates for the calculated models are compared.
This model is easy to specify and results in meaningful fit
statistics and standard errors. However, the division into
sub-samples is most often problematic, because it conflicts with
the assumption of a normal distribution. For example, a median
split cuts the sample into a high and a low half, but by doing so
also takes away the lower part and the upper part, respectively,
of the distribution. Thus, the data is not distributed normally
anymore. This is problematic, as statistical methods rely on the
assumption of a normal distribution.
The indicant product approach is another way to look at latent
interaction effects. In this case, we create an interaction latent
variable. This avoids the median split problems discussed above
and yields more accurate point estimates for linear interaction
effects. However, this model is more difficult to specify, needs
more information to be identfied and and is more difficult to
converge, as greater starting values are needed. In the output of
the model, the interaction term is accurate, but the fit
statistics (e.g., χ2, RMSEA) become meaningless and the standard
errors are off.
8. The great advantages of MACS over a standard t-test and an
ANOVA are the advantages of SEM in general. That is, we can
compare differences between the two groups in our two-group
research design on a latent level. In SEM we can correct for
measurement error and differences in variances among groups. Thus,
we yield much more accurate results. In particular, latent means
used in SEM are much better indices of mean level differences than
indicator means used in regular t-tests or ANOVAs.
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