Title:  Profile likelihood-based confidence regions for Structural Equation Models.

 

Abstract:  Structural equation models (SEM) are often employed to evaluate a network of directional and non-directional relationships between latent and measured variables, where inference typically concerns multiple parameters. The common approach of using one-at-a-time Wald methods (tests and confidence intervals) has two limitations. First, Wald methods do not have optimal properties in SEM. Second, one-at-a-time methods are inappropriate for inference about multiple parameters. The talk will begin with a review of Wald and likelihood-based methods for inference. Then, a framework of computing exact profile likelihood-based confidence regions (CRs) for SEM is outlined. Using a published example on a latent variable mediation about the effect of perceived discrimination on psychological well-being, with in-group identification as the mediator, we illustrate the advantages of using likelihood-based CRs over Wald-type CRs. We conclude with some general recommendations for multi-parameter inference in SEM.