From missing data to informative GPA predictions: Navigating selection process beliefs with the partial identifiability approach

The extent to which college admissions test scores can forecast college grade point average (GPA) is often evaluated in predictive validity studies using regression analyses. A problem in college admissions processes is that we observe test scores for all the applicants; however, we cannot observe the GPA of applicants who were not selected. The standard solution to tackle this problem has relied upon strong assumptions to identify the exact value of the regression function in the presence of missing data. In this paper, we present an alternative approach based on the theory of partial identifiability that considers a variety of milder assumptions to learn about the regression function. Using a university admissions dataset we illustrate how results can vary as a function of the assumptions that one is willing to make about the selection process.