Loss Function Based Ranking in Two-Stage, Hierarchical Models

Rongheng Lin, Johns Hopkins University Bloomberg School of Public Health
Thomas A. Louis, Johns Hopkins University Bloomberg School of Public Health
Susan M. Paddock, RAND
Greg Ridgeway, RAND

Abstract

Several authors have studied the performance of optimal, squared error loss (SEL) estimated ranks. Though these are effective, in many applications interest focuses on identifying the relatively good (e.g., in the upper 10%) or relatively poor performers. We construct loss functions that address this goal and evaluate candidate rank estimates, some of which optimize specific loss functions. We study performance for a fully parametric hierarchical model with a Gaussian prior and Gaussian sampling distributions, evaluating performance for several loss functions. Results show that though SEL-optimal ranks and percentiles do not specifically focus on classifying with respect to a percentile cut point, they perform very well over a broad range of loss functions. We compare inferences produced by the candidate estimates using data from The Community Tracking Study.