Bayesian analysis of structural equation models with dichotomous variables

Abstract

Structural equation modelling has been used extensively in the behavioural and social sciences for studying interrelationships among manifest and latent variables. Recently, its uses have been well recognized in medical research. This paper introduces a Bayesian approach to analysing general structural equation models with dichotomous variables. In the posterior analysis, the observed dichotomous data are augmented with the hypothetical missing values, which involve the latent variables in the model and the unobserved continuous measurements underlying the dichotomous data. An algorithm based on the Gibbs sampler is developed for drawing the parameters values and the hypothetical missing values from the joint posterior distributions. Useful statistics, such as the Bayesian estimates and their standard error estimates, and the highest posterior density intervals, can be obtained from the simulated observations. A posterior predictive p-value is used to test the goodness-of-fit of the posited model. The methodology is applied to a study of hypertensive patient non-adherence to medication.

Spatial self-selection in land-use–travel behavior interactions: accounting simultaneously for attitudes and socioeconomic characteristics

“…The predictive posterior p is a Bayesian counterpart to the classic p-value, and since it uses posterior predictive replications of the data, it is able to measure directly the discrepancy between the sample and the population quantities (Meng 1994). Thus, it can be used to test if the proposed model is either plausible or not (Lee and Song 2003). Lee and Song (2003) argue that if the predictive posterior p is close to 0 or 1, then the null hypothesis, stating that the model is plausible, should be rejected.…”

“…Thus, it can be used to test if the proposed model is either plausible or not (Lee and Song 2003). Lee and Song (2003) argue that if the predictive posterior p is close to 0 or 1, then the null hypothesis, stating that the model is plausible, should be rejected. For values not far off 0.5, the model can be considered as plausible and therefore accepted (Lee 2007).…”

Entrepreneurial decisions: Insights into the use of support services for new business creation

“…Structural equation models are regression models with observed and latent variables (Lee, 2007) that explain multiple interrelations among variables (Hair et al, 2010). Due to the ordinal and interval nature of the variables taken into consideration (Albert & Chib, 1993;Lee & Song, 2003), we have used a Bayesian approach to estimate the parameters of the model. By means of Markov chains and Monte Carlo methods, Bayesian estimation also allows sample replication, making it especially appropriate and reliable for relatively small samples (Lee, 2007: 5), like this available here.…”

A spatial structural equation modelling framework for health count responses

“…. , x i M ) one may use an exploratory approach, or a confirmatory one in which some elements in the M × A matrix = [ am ] are set to zero in line with substantive knowledge [15]. Both the spatially structured residual effects S and latent social constructs X follow a multivariate conditionally autoregressive or MCAR prior [16].…”