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A zero‐ and K ‐inflated mixture model for health questionnaire data
Author(s) -
Finkelman Matthew D.,
Green, Jennifer Greif,
Gruber Michael J.,
Zaslavsky Alan M.
Publication year - 2011
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4217
Subject(s) - item response theory , zero (linguistics) , psychology , population , expectation–maximization algorithm , statistics , mixture model , trait , econometrics , component (thermodynamics) , clinical psychology , psychiatry , mathematics , maximum likelihood , psychometrics , computer science , medicine , linguistics , philosophy , physics , environmental health , thermodynamics , programming language
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. Copyright © 2011 John Wiley & Sons, Ltd.