A General Structural Equation Model with Dichotomous, Ordered Categorical, and Continuous Latent Variable Indicators

1984/03/01 by Bengt Muthén · 2,040 citations
Agricultural and Biological Sciences · Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Categorical variable #Correlation #Econometrics #Estimator #Jackknife resampling #Latent variable #Latent variable model #Mathematics #Multi-Criteria Decision Making #Multivariate statistics #Ordered probit #Polychoric correlation #Sensory Analysis and Statistical Methods #Statistics #Structural equation modeling #Variable (mathematics)

paper · doi:10.1007/bf02294210

published in Psychometrika 49(1), 115-132 (Springer Science+Business Media)

openalex publication_date 1984/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

A structural equation model is proposed with a generalized measurement part, allowing for dichotomous and ordered categorical variables (indicators) in addition to continuous ones. A computationally feasible three-stage estimator is proposed for any combination of observed variable types. This approach provides large-sample chi-square tests of fit and standard errors of estimates for situations not previously covered. Two multiple-indicator modeling examples are given. One is a simultaneous analysis of two groups with a structural equation model underlying skewed Likert variables. The second is a longitudinal model with a structural model for multivariate probit regressions.

Citations

• Maximum Likelihood Estimation of the Polychoric Correlation Coefficient

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