Modelling individual response time effects between and within experimental speed conditions: A GLMM approach for speeded tests

Completing test items under multiple speed conditions avoids the performance measure being confounded with individual differences in the speed–accuracy compromise, and offers insights into the response process, that is, how response time relates to the probability of a correct response. This relation is traditionally represented by two conceptually different functions: the speed-accuracy trade-off function (SATF) across conditions relating the condition average response time to the condition average of accuracy, and the conditional accuracy function (CAF) within a condition describing accuracy conditional on response time. Using a generalized linear mixed modelling approach, we propose an item response modelling framework that is suitable for item response and response time data from experimental speed conditions. The proposed SATF and CAF model accommodates response time effects between conditions (i.e., person and item SATF slope) and within conditions (i.e., residual CAF slopes), captures person and item differences in these effects, and is suitable for measures with a strong speed component. Moreover, for a single condition a CAF model is proposed distinguishing person, item and residual CAF. The properties of the models are illustrated with an empirical example.