Was there a riverside miracle? A hierarchical framework for evaluating programs with grouped data

This article discusses the evaluation of programs implemented at multiple sites. Two frequently used methods are pooling the data or using fixed effects (an extreme version of which estimates separate models for each site). The former approach ignores site effects. The latter incorporates site effects but lacks a framework for predicting the impact of subsequent implementations of the program (e.g., would a new implementation resemble Riverside?). I present a hierarchical model that lies between these two extremes. Using data from the Greater Avenues for Independence demonstration, I demonstrate that the model captures much of the site-to-site variation of the treatment effects but has less uncertainty than estimating the treatment effect separately for each site. I also show that when predictive uncertainty is ignored, the treatment impact for the Riverside sites is significant, but when predictive uncertainty is considered, the impact for these sites is insignificant. Finally, I demonstrate that the model extrapolates site effects with reasonable accuracy when the site being predicted does not differ substantially from the sites already observed. For example, the San Diego treatment effects could have been predicted based on their site characteristics, but the Riverside effects are consistently underpredicted.