When these models involve latent variables and the corresponding observed measurements, we can test whether those measurements are invariant across groups. We naturally have hypotheses regarding differences in parameters across groups when fitting structural equation models as well. For regression models, this can be as simple as including group indicators in the model and interacting them with other predictors. In other words, we may wish to perform tests of moderation when the moderator variable is categorical. ![]() When fitting almost any model, we may be interested in investigating whether parameters differ across groups such as time periods, age groups, gender, or school attended.
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