, Volume 78, Issue 4, pp 624–647

A Bayesian Modeling Approach for Generalized Semiparametric Structural Equation Models


  • Xin-Yuan Song
    • Department of StatisticsThe Chinese University of Hong Kong
  • Zhao-Hua Lu
    • Department of StatisticsThe Chinese University of Hong Kong
    • Department of StatisticsSun Yat-sen University
  • Edward Hak-Sing Ip
    • Department of Biostatistical Sciences, Division of Public Health SciencesWake Forest University Health Sciences

DOI: 10.1007/s11336-013-9323-7

Cite this article as:
Song, X., Lu, Z., Cai, J. et al. Psychometrika (2013) 78: 624. doi:10.1007/s11336-013-9323-7


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.

Key words

Bayesian P-splineslatent variablesMCMC methodssemiparametric models

Copyright information

© The Psychometric Society 2013