Was there a Riverside miracle? An hierarchical framework for evaluating programs with grouped data

This paper uses data from the Greater Avenues for Independence (GAIN) demonstration to discuss the evaluation of programs that are 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, however, ignores site effects. Though the latter incorporates site effects, it lacks a framework for predicting the impact of subsequent implementations of the program (e.g., will a new implementation resemble Riverside or Alameda?). I present an hierarchical model that lies between these two extremes. For the GAIN data, I demonstrate that the model captures much of the site-to-site variation of treatment effects, but has less uncertainty than a model which estimates treatment effects separately for each site. I also show that uncertainty in predicting site effects is important: when the predictive uncertainty is ignored, the treatment impact for the Riverside sites is significant, but when we consider predictive uncertainty, the impact for the Riverside sites is insignificant. Finally, I demonstrate that the model is able to extrapolate site effects with reasonable accuracy, when the site for which the prediction is being made does not differ substantially from the sites already observed. For example, the San Diego treatment effects could have been predicted based on observable site characteristics, but the Riverside effects are consistently underestimated.