In spatial epidemiology studies, the effects of covariates on adverse health outcomes could vary over space and time so examining the spatio-temporally varying effects is useful. In particular, the association between covariates and health outcomes could have locally different temporal patterns. In this article, we develop a Bayesian spatio-temporal latent model to identify spatial clusters in each of which covariate effects have homogeneous temporal patterns as well as estimate heterogeneous temporal effects of covariates depending on spatial groups. We compare the proposed model to several alternative models to assess the performance of the proposed model in terms of a range of model assessment measures. Low birth weight incidence data in Georgia for the years 1997-2006 are used.