A Bivariate Generalized Linear Item Response Theory Modeling Framework to the Analysis of Responses and Response Times

A generalized linear modeling framework to the analysis of responses and response times is outlined. In this framework, referred to as bivariate generalized linear item response theory (B-GLIRT), separate generalized linear measurement models are specified for the responses and the response times that are subsequently linked by cross-relations. The cross-relations can take various forms. Here, we focus on cross-relations with a linear or interaction term for ability tests, and cross-relations with a curvilinear term for personality tests. In addition, we discuss how popular existing models from the psychometric literature are special cases in the B-GLIRT framework depending on restrictions in the cross-relation. This allows us to compare existing models conceptually and empirically. We discuss various extensions of the traditional models motivated by practical problems. We also illustrate the applicability of our approach using various real data examples, including data on personality and cognitive ability.