Estimating New Quantities from Longitudinal Test Scores to Improve Forecasts of Future Performance

Psychometric models for longitudinal test scores typically estimate quantities associated with single-administration tests, like ability at each time-point. However, models for longitudinal tests have not considered opportunities to estimate new quantities that are unavailable from single-administration tests. Specifically, we discuss dynamic measurement models - which combine aspects of longitudinal IRT, nonlinear growth models, and dynamic assessment - to directly estimate capacity, defined as the expected future score once the construct has fully developed. After discussing the history and connecting these areas into a single framework, we apply the model to verbal test scores from the Intergenerational Studies, which follow 494 people from 3 to 72 years old. The goal is to predict adult verbal scores (Age ≥ 34) from adolescent scores (Age ≤ 20). We held-out the adult data for prediction and compared predictions from traditional longitudinal IRT ability scores and proposed dynamic measurement capacity scores from models fit to the adolescent data. Results showed that the R² from capacity scores were 2.5 times larger than the R² from longitudinal IRT ability scores (43% vs. 16%), providing some evidence that exploring new quantities available from longitudinal testing could be worthwhile when an interest in testing is forecasting future performance.