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A Bayesian Modeling Approach for Generalized Semiparametric Structural Equation Models

Published online by Cambridge University Press:  01 January 2025

Xin-Yuan Song ,
Zhao-Hua Lu ,
Jing-Heng Cai  and
Edward Hak-Sing Ip
Xin-Yuan Song
Affiliation:
Department of Statistics, The Chinese University of Hong Kong
Zhao-Hua Lu
Affiliation:
Department of Statistics, The Chinese University of Hong Kong
Jing-Heng Cai*
Affiliation:
Department of Statistics, Sun Yat-sen University
Edward Hak-Sing Ip
Affiliation:
Department of Biostatistical Sciences, Division of Public Health Sciences, Wake Forest University Health Sciences
*
Requests for reprints should be sent to Jing-Heng Cai, Department of Statistics, Sun Yat-sen University, Guangzhou, China. E-mail: caijheng@mail.sysu.edu.cn
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Abstract

In behavioral, biomedical, and psychological studies, structural equation models (SEMs) have been widely used for assessing relationships between latent variables. Regression-type structural models based on parametric functions are often used for such purposes. In many applications, however, parametric SEMs are not adequate to capture subtle patterns in the functions over the entire range of the predictor variable. A different but equally important limitation of traditional parametric SEMs is that they are not designed to handle mixed data types—continuous, count, ordered, and unordered categorical. This paper develops a generalized semiparametric SEM that is able to handle mixed data types and to simultaneously model different functional relationships among latent variables. A structural equation of the proposed SEM is formulated using a series of unspecified smooth functions. The Bayesian P-splines approach and Markov chain Monte Carlo methods are developed to estimate the smooth functions and the unknown parameters. Moreover, we examine the relative benefits of semiparametric modeling over parametric modeling using a Bayesian model-comparison statistic, called the complete deviance information criterion (DIC). The performance of the developed methodology is evaluated using a simulation study. To illustrate the method, we used a data set derived from the National Longitudinal Survey of Youth.

Keywords

Bayesian P-splineslatent variablesMCMC methodssemiparametric models
Type
Original Paper
Information
Psychometrika , Volume 78 , Issue 4 , October 2013 , pp. 624 - 647
Copyright
Copyright © 2013 The Psychometric Society

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