## Application 6: Testing for Invariant Factorial Structure of a Theoretical Construct (First-Order CFA Model)

In seeking evidence of multigroup 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 you with specific examples of how each of these questions can be answered using structural equation modeling based on LISREL 8.