A Zero-Inflated Box-Cox Normal Unipolar Item Response Model for Measuring Constructs of Psychopathology
Applied Psychological Measurement
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.
Magnus, Brooke E. and Liu, Yang, "A Zero-Inflated Box-Cox Normal Unipolar Item Response Model for Measuring Constructs of Psychopathology" (2018). Psychology Faculty Research and Publications. 424.
ADA accessible version
Accepted version. Applied Psychological Measurement, Vol. 42, No. 7 (October 1, 2018): 571-589. DOI. © 2018 SAGE. Used with permission.