A Zero-Inflated Box-Cox Normal Unipolar Item Response Model for Measuring Constructs of Psychopathology

This research introduces a latent class item response theory (IRT) approach for modeling item response data from zero-inflated, positively skewed, and arguably unipolar constructs of psychopathology. As motivating data, the authors use 4,925 responses to the Patient Health Questionnaire (PHQ-9), a nine Likert-type item depression screener that inquires about a variety of depressive symptoms. First, Lucke's log-logistic unipolar item response model is extended to accommodate polytomous responses. Then, a nontrivial proportion of individuals who do not endorse any of the symptoms are accounted for by including a nonpathological class that represents those who may be absent on or at some floor level of the latent variable that is being measured by the PHQ-9. To enhance flexibility, a Box-Cox normal distribution is used to empirically determine a transformation parameter that can help characterize the degree of skewness in the latent variable density. A model comparison approach is used to test the necessity of the features of the proposed model. Results suggest that (a) the Box-Cox normal transformation provides empirical support for using a log-normal population density, and (b) model fit substantially improves when a nonpathological latent class is included. The parameter estimates from the latent class IRT model are used to interpret the psychometric properties of the PHQ-9, and a method of computing IRT scale scores that reflect unipolar constructs is described, focusing on how these scores may be used in clinical contexts.