A Zero- and K-Inflated Mixture Model for Health Questionnaire Data

Publication Name: 
Statistics in Medicine
Publication Authors: 
Finkelman M, Green JG, Gruber MJ, et al.
HCP Authors:Alan Zaslavsky PhD
Date of Publication: 
Apr 2011

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.

PMC ID: PMC3086029 (April 30, 2011)

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