Estimating Test-Retest Reliability in the Presence of Self-Selection Bias and Learning/Practice Effects

Test-retest reliability is often estimated using naturally occurring data from test repeaters. In settings such as admissions testing, test takers choose if and when to retake an assessment. This self-selection can bias estimates of test-retest reliability because individuals who choose to retest are typically unrepresentative of the broader testing population and because differences among test takers in learning or practice effects may increase with time between test administrations. We develop a set of methods for estimating test-retest reliability from observational data that can mitigate these sources of bias, which include sample weighting, polynomial regression, and Bayesian model averaging. We demonstrate the value of using these methods for reducing bias and improving precision of estimated reliability using empirical and simulated data, both of which are based on more than 40,000 repeaters of a high-stakes English language proficiency test. Finally, these methods generalize to settings in which only a single, error-prone measurement is taken repeatedly over time and where self-selection and/or changes to the underlying construct may be at play.