Combining Information from Related Regressions

Abstract:

In this paper we consider the problem of combining information from several regression studies, each considering only a subset of the variables of interest. We approached the problem using Bayesian hierarchical models. These combine flexibility in modelling study-to-study as well as within study variability with reliable computational algorithms for variance components and imputation of missing values. We provide full conditional distributions for the implementation of a block Gibbs sampler, useful for arbitrary patterns of variables missing by study. We discuss an application to investigating the relation between chlorophyll-a and phosphorus in twelve North temperate lakes by using data from the literature. An important covariate is nitrogen, which is reported only in some of the studies.

Key words:

Data augmentation, Markov chain Monte Carlo, meta-analysis, random effects, simulation.