Spatio-temporal analysis of small area health data often involves choosing a fixed set of predictors prior to the final model fit. In this paper, we propose a spatio-temporal approach of Bayesian model selection to implement model selection for certain areas of the study region as well as certain years in the study time line. Here, we examine the usefulness of this approach by way of a large-scale simulation study accompanied by a case study. Our results suggest that a special case of the model selection methods, a mixture model allowing a weight parameter to indicate if the appropriate linear predictor is spatial, spatio-temporal, or a mixture of the two, offers the best option to fitting these spatio-temporal models. In addition, the case study illustrates the effectiveness of this mixture model within the model selection setting by easily accommodating lifestyle, socio-economic, and physical environmental variables to select a predominantly spatio-temporal linear predictor.