An important class of applications of measurement error or constrained factor
analytic models consists of comparing models for several populations. In such
cases it is appropriate to make explicit statistical tests of model similarity across
groups and to constrain some model parameters to be equal across groups using
a priori substantive information. This article discusses a statistical model devel
oped by Jöreskog for these purposes. The model is applied to children's and
parents' reports of parental socioeconomic statuses for several grade levels.
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