Structural equation models (SEM) are widely used for modeling complex multivariate relationships among measured and latent variables. Although several analytical approaches to interval estimation in SEM have been developed, there lacks a comprehensive review of these methods. We review the popular Wald-type and lesser known likelihood-based methods in linear SEM, emphasizing profile likelihood-based confidence intervals (CIs). Existing algorithms for computing profile likelihood-based CIs are described, including two newer algorithms which are extended to construct profile likelihood-based confidence regions (CRs). Finally, we illustrate the use of these CIs and CRs with two empirical examples, and provide practical recommendations on when to use Wald-type CIs and CRs versus profile likelihood-based CIs and CRs. OpenMx example code is provided in an Online Appendix for constructing profile likelihood-based CIs and CRs for SEM.
