A binary latent variable is constructed to account for the correlation between multiple binary outcomes and is treated as a dependent variable in modelling for covariate effects. This modelling method is similar to the structural equation modelling. Three models are considered: (1) all covariates affecting the binary latent variable directly; (2) some covariates affecting the binary latent variable while other affecting the manifestation of the binary outcomes; and (3) no covariates are included. Gibbs sampling, a special case of the Markov Chain Monte Carlo method, is used to estimate the parameters in the models. Simulation studies show that this method is valid and reliable in estimating covariate effects. But Model (1) fitted the data best with lowest value in the deviance information criteria. The method is illustrated by applying it to the data analysis of an environmental air pollution study. The results show that air pollution (i.e. the most versus the least polluted district) (odds ratio 1.20; 95% confidence interval 0.97-1.49; p=0.102), smoking (relative to not smoking) (2.75; 2.21-3.41; p < 0.001) and mosquito coil use (relative to non-use) (1.27; 0.99-1.62; p=0.058) had an impact on the respiratory health of male adults in Hong Kong.
Copyright 2004 John Wiley & Sons, Ltd.