A two‐stage estimation of structural equation models with continuous and polytomous variables

Key Points

• To develop and evaluate a computationally efficient two-stage estimation framework for structural equation models containing both continuous and polytomous variables.
• Implemented a partition maximum likelihood approach in the first stage to estimate thresholds alongside polyserial and polychoric correlations.
• Applied a generalized least squares procedure in the second stage using the joint asymptotic distribution and a weight matrix to estimate structural parameters.
• Conducted simulation experiments to assess asymptotic statistical properties, empirical behavior, robustness, and comparative efficiency against existing methods.
• Derived the formal joint asymptotic distribution and theoretical properties for the first- and second-stage structural estimators.
• Simulation results demonstrated that the proposed two-stage procedure achieves computational efficiency and robust estimation across mixed continuous and polytomous data.