Multivariate hierarchical Bayesian models and choice of priors in the analysis of survey data

Multivariate regression models, i.e. regression models where the left-hand side of the regression equation denotes a matrix of dependent variables, have long been developed. However, the statistical analysis of empirical data is usually restricted to multivariable regression methods with only one dependent variable. Within the framework of hierarchical Bayesian methods, the present study illustrates (i) how multivariate regression models offer new possibilities of information synthesis and theory testing in survey data analysis, and (ii) how sensitive the results are to different specifications of prior distributions. To this end, a large representative survey is utilized to specify two multivariate hierarchical Bayesian regression models $ (N = 39,280) $ (N=39,280) which are calculated under two different prior distribution specifications. The estimation procedures and their implementation in R are described, convergence and predictive power analysis of each model are presented, and the advantages and disadvantages of multivariate regression methods are discussed. In general, the results obtained under each prior specification are to some extent similar, although differences were observed regarding model complexity, efficiency and predictive power. It is concluded that these methods facilitate the development and testing of complex research hypotheses, and are promising alternatives to a more efficient data analysis of large survey data sets.