Multiple Groups

SEM can be applied to a single group or multiple groups. When analyzing multiple groups all parameters in a model (i.e., means, variances, and path coefficients) may be compared between groups. The general approach is to compare two models: one where the parameter or parameters of interest are specified to be equal between groups, we say constrained equal, and another model which allows the parameters to vary between groups. Each model is associated with a x 2 test of model fit. Importantly, these models are nested; the model with constrained parameters is nested within the more general model. In this fashion, groups can be compared on many different dimensions without restrictive assumptions. For instance, recall how in the analysis of variance when we compare group means we assume their variances are equal. With multiple group SEM we can compare means in the presence of unequal variances.

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