Comparing Methods of Maximum Likelihood and Unweighted Least-Squares Estimation Across Structural Equation Modeling Software Programs

• Authors: Fred B. Bryant and Albert Satorra
• Structural Equation Modeling: A Multidisciplinary Journal, September 2025.

It is highly desirable that the results of analyses be equivalent, regardless of the software program researchers use to analyze their data. To assess cross-program comparability, we used the latest versions of four leading SEM programs—LISREL, EQS, Mplus, and R-lavaan—to conduct confirmatory factor analysis of responses to a popular measure of optimism (N = 803), using two methods of estimation (maximum likelihood and unweighted least-squares) and two methods of inference (normal-theory and robust). When using default ML estimation with either normal-theory or robust inference, all four programs produced equivalent parameter estimates, standard errors, and χ² values. When using ULS estimation, parameter estimates were equivalent, but there was one marked difference across programs in normal-theory inference and several marked differences in robust test statistics. Pinpointing such discrepancies, even if they occur using nondefault options, benefits SEM users and helps promote uniformity in results across SEM programs.