What Do We Learn from Graduate Admissions Committees? A Multiple Rater, Latent Variable Model, with Incomplete Discrete and Continuous Indicators

What do we really know about applicants to graduate school? How much information is in an applicant's file? What do we learn by having graduate admissions committees read and score applicant files? In this article, I develop a statistical model for measuring applicant quality, combining the information in the committee members' ordinal ratings with the information in applicants' GRE scores. The model produces estimates of applicant quality purged of the influence of committee members' preferences over ostensibly extraneous applicant characteristics, such as gender and intended field of study. An explicitly Bayesian approach is adopted for estimation and inference, making it straightforward to obtain confidence intervals not only on latent applicant quality but over rank orderings of applicants and the probability of belonging in a set of likely admittees. Using data from applications to a highly ranked political science graduate program, I show that there is considerable uncertainty in estimates of applicant quality, making it impossible to make authoritative distinctions as to quality among large portions of the applicant pool. The multiple rater model I develop here is extremely flexible and has applications in fields as diverse as judicial politics, legislative politics, international relations, and public opinion.