Modeling the Intraindividual Relation of Ability and Speed within a Test

Understanding the intraindividual relation between an individual's speed and ability in testing scenarios is essential to assure a fair assessment. Different approaches exist for estimating this relationship, that either rely on specific study designs or on specific assumptions. This paper aims to add to the toolbox of approaches for estimating this relationship. We propose the intraindividual speed-ability-relation (ISAR) model, which relies on nonstationarity of speed and ability over the course of the test. The ISAR model explicitly models intraindividual change in ability and speed within a test and assesses the intraindividual relation of speed and ability by evaluating the relationship of both latent change variables. Model estimation is good, when there are interindividual differences in speed and ability changes in the data. In empirical data from PISA, we found that the intraindividual relationship between speed and ability is not universally negative for all individuals and varies across different competence domains and countries. We discuss possible explanations for this relationship.