A Box–Cox normal model for response times

Abstract

The log-transform has been a convenient choice in response time modelling on test items. However, motivated by a dataset of the Medical College Admission Test where the lognormal model violated the normality assumption, the possibilities of the broader class of Box-Cox transformations for response time modelling are investigated. After an introduction and an outline of a broader framework for analysing responses and response times simultaneously, the performance of a Box-Cox normal model for describing response times is investigated using simulation studies and a real data example. A transformation-invariant implementation of the deviance information criterium (DIC) is developed that allows for comparing model fit between models with different transformation parameters. Showing an enhanced description of the shape of the response time distributions, its application in an educational measurement context is discussed at length.