A Bayesian Modeling Approach for Generalized Semiparametric Structural Equation Models
- PDF / 461,131 Bytes
- 24 Pages / 504 x 720 pts Page_size
- 44 Downloads / 208 Views
2013 DOI : 10.1007/ S 11336-013-9323-7
A BAYESIAN MODELING APPROACH FOR GENERALIZED SEMIPARAMETRIC STRUCTURAL EQUATION MODELS
X IN -Y UAN S ONG AND Z HAO -H UA L U DEPARTMENT OF STATISTICS, THE CHINESE UNIVERSITY OF HONG KONG
J ING -H ENG C AI DEPARTMENT OF STATISTICS, SUN YAT-SEN UNIVERSITY
E DWARD H AK -S ING I P DEPARTMENT OF BIOSTATISTICAL SCIENCES, DIVISION OF PUBLIC HEALTH SCIENCES, WAKE FOREST UNIVERSITY HEALTH SCIENCES 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-splines, latent variables, MCMC methods, semiparametric models.
1. Introduction As an analytic tool deeply rooted in the psychological and social sciences, the structural equation model (SEM; Bollen, 1989; Lee, 2007) is one of the most widely used methods for assessing plausible causal assumptions through the modeling of relationships between latent variables. SEMs have found broad applications in various disciplines including psychology, social studies, economics, and medicine (see, for example, Bentler & Stein, 1992; Pugesek, Tomer, & von Eye, 2003; Sanchez, Budtz-Jorgenger, Ryan, & Hu, 2005, among others). Briefly, an SEM consists of two components—the measurement component is a factor-analysis model that groups correlated observed variables into the corresponding latent variables; the structural component is a set of regression equations that assess the effects of explanatory latent variables on outcome latent variables. It is possible for an SEM to have a set of outcome variables acting as regressors on another set of outcome variables. A salient feature of the SEM is its ability to account for measurement error in the model. By constructing latent variables to represent
Data Loading...
