The continuous G-DINA model and the Jensen-Shannon divergence

Abstract

Interest in diagnostic assessment has grown rapidly in recent years, as the public has increasingly looked to assessments to enhance educational outcomes. As a result, cognitive diagnosis models (CDMs) have been a popular subject for psychometric researchers. The goal of this research is to expand the methodological toolbox for CDMs by offering two new developments. First, we introduce a generalization of a recently proposed CDM, the continuous-DINA (C-DINA; Minchen, de la Torre, & Liu, under review) model. These models handle continuous response data, rather than binary or polytomous data, allowing for CDMs to be estimated from different kinds of data, such as response times or probability testing. Second, we adapt the Jensen-Shannon Divergence (JSD; Lin, 1991), which is based on the Shannon Entropy and is a measure of quantifying the divergence between two or more probability distributions, for use as an item selection algorithm in cognitive diagnostic computerized adaptive testing. Existing indices, such as those proposed in Kaplan, de la Torre, & Barrada (2015) are insufficient for various reasons. Finally, we conduct two simulation studies. The first establishes the viability of the C-G-DINA model by determining the robustness of model parameter estimation to a variety of different conditions. The second is designed to show the extent to which the JSD selection index provides a substantial improvement over random item selection in terms of examinee classification and test length (for variable stopping rule conditions) across a range of conditions.