Latent Variable Models with Mixed Continuous and Polytomous Data

Jian-Qing Shi · Sik‐Yum Lee

108 citations0/0 files storedJournal of the Royal Statistical Society Series B (Statistical Methodology)

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Psychometric Methodologies and Testing Statistical Methods and Bayesian Inference Bayesian Methods and Mixture Models

Abstract

Summary Owing to the nature of the problems and the design of questionnaires, discrete polytomous data are very common in behavioural, medical and social research. Analysing the relationships between the manifest and the latent variables based on mixed polytomous and continuous data has proven to be difficult. A general structural equation model is investigated for these mixed outcomes. Maximum likelihood (ML) estimates of the unknown thresholds and the structural parameters in the covariance structure are obtained. A Monte Carlo–EM algorithm is implemented to produce the ML estimates. It is shown that closed form solutions can be obtained for the M-step, and estimates of the latent variables are produced as a by-product of the analysis. The method is illustrated with a real example.

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References

1993Lisrel 8: Structural Equation Modeling With the Simplis Command Language 1984A General Structural Equation Model with Dichotomous, Ordered Categorical, and Continuous Latent Variable Indicators 2004Latent Variable Models 1978Structural Analysis of Covariance and Correlation Matrices 1993Item Response Theory: Parameter Estimation Techniques.1980Linear Structural Equations with Latent Variables 1983Some Contributions to Efficient Statistics in Structural Models: Specification and Estimation of Moment Structures 1994Item Response Theory: Parameter Estimation Techniques.

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2002Maximum Likelihood Estimation of Nonlinear Structural Equation Models 2001Bayesian estimation and test for factor analysis model with continuous and polytomous data in several populations 2005A MULTIVARIATE PROBIT LATENT VARIABLE MODEL FOR ANALYZING DICHOTOMOUS RESPONSES

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