Rethinking Ordinal Variable Identification in Weighted Least Squares Structural Equation Modeling

Weighted least squares (WLS) estimation has tremendous utility for structural equation models (SEMs) that include ordered categorical data. However, some common statistical programs for fitting these models lack full flexibility in specification. Moreover, the popular approach toward model identification of ordinal variables arbitrarily constrains researchers and limits their ability to construct theories involving ordinal data. We develop a novel approach for identifying SEMs with ordered categorical variables that allows a wider variety of model specifications and theories, furthermore implementing this approach in OpenMx. We review WLS and ordinal variables both in general and as implemented in common software programs. Then we discuss the novel approach taken by the OpenMx implementation and derive analytic criteria for ordinal data identification. We conclude by posing new research questions that may now be addressed.