ABSTRACT
In seeking evidence ofmultigroup invariance, researchers are typically interested in finding the answer to one of five questions. First, do the items comprising a particular measuring instrument operate equivalently across different populations (e.g., gender, age, ability)? In other words, is the measurement model group-invariant? Second, is the factorial structure of a single instrument, or of a theoretical construct measured by multiple instruments, equivalent across populations? Here, invariance of the structural model is of primary interest and, in particular, the equivalency of relations among the theoretical constructs. Third, are certain paths in a specified causal structure invariant across populations? Fourth, are the latent means of particular constructs in a model different across populations? Finally, does the factorial structure of a measuring instrument replicate across independent samples of the same population? This latter question, of course, addresses the issue of cross-validation. Applications presented in the next four chapters provide spe-
stringent than is the case for tests of invariance related to sets of parameters in the model (Muth{m, personal communication, October 1988). Indeed, Muthen contended that the omnibus test provides little guidance in testing for equality across groups and thus should not be regarded as a necessary prerequisite to the testing of more specific hypotheses related to group invariance.
