Abstract

The hierarchical Bayesian method combines and summarizes the results from multiple sites using a weighted regression analysis where the unit of observation is the site, and the covariates are characteristics of the sites. There are two sources of random error in this model: the usual within-site sampling error and an additional random effect due to unpredictable differences among sites. The hierarchical model allows sites with small sample sizes to "borrow strength" from the others, to the extent that the between-site variance is estimated to be small. A special graph, called a trace plot, displays the posterior distribution of the among-site standard deviation and its effect on the other parameter estimates. This paper combines and re-analyzes data on schizophrenic births collected across seventeen states of the U.S. We found additional evidence that severe weather may be associated with increased risk of schizophrenia and confirmed the existence of a dose-response curve, where the risk for schizophrenia increases as severity of winter increases.

Citations