title: A zero- and K-inflated mixture model for health questionnaire data.
abstract: In psychiatric assessment, Item Response Theory (IRT) is a popular tool to formalize the relation between the severity of a disorder and the associated responses to questionnaire items. Practitioners of IRT sometimes make the assumption of normally distributed severities within a population; while convenient, this assumption is often violated when measuring psychiatric disorders. Specifically, there may be a sizable group of respondents whose answers place them at an extreme of the latent trait spectrum. In this article, a zero- and K-inflated mixture model is developed to account for the presence of such respondents. The model is fitted using an expectation-maximization (E-M) algorithm to estimate the percentage of the population at each end of the continuum, concurrently analyzing the remaining 'graded component' via IRT. A method to perform factor analysis for only the graded component is introduced. In assessments of oppositional defiant disorder and conduct disorder, the zero- and K-inflated model exhibited better fit than the standard IRT model.
authors.affiliation: Tufts University School of Dental Medicine, Boston, MA, USA. matthew.finkelman@tufts.edu
authors.forename: Matthew D
authors.initials: MD
authors.lastname: Finkelman
authors.forename: Jennifer Greif
authors.initials: JG
authors.lastname: Green
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Gruber
authors.forename: Alan M
authors.initials: AM
authors.lastname: Zaslavsky
mesh_terms: D000293:Adolescent; D000465:Algorithms; D019958:Attention Deficit and Disruptive Behavior Disorders / Q000175:diagnosis / Q000523:psychology; D019955:Conduct Disorder / Q000175:diagnosis / Q000523:psychology; D005163:Factor Analysis, Statistical; D006801:Humans; D008960:Models, Psychological; D015233:Models, Statistical; D010290:Parents; D011795:Surveys and Questionnaires