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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\u2010 and<jats:italic>K<\/jats:italic>\u2010inflated mixture model is developed to account for the presence of such respondents. The model is fitted using an expectation\u2013maximization (E\u2010M) algorithm to estimate the percentage of the population at each end of the continuum, concurrently analyzing the remaining \u2018graded component\u2019 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\u2010 and<jats:italic>K<\/jats:italic>\u2010inflated model exhibited better fit than the standard IRT model. Copyright \u00a9 2011 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/sim.4217","type":"journal-article","created":{"date-parts":[[2011,3,2]],"date-time":"2011-03-02T02:44:36Z","timestamp":1299033876000},"page":"1028-1043","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["A zero\u2010 and<i>K<\/i>\u2010inflated mixture model for health questionnaire data"],"prefix":"10.1002","volume":"30","author":[{"given":"Matthew D.","family":"Finkelman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jennifer Greif","family":"Green,","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael J.","family":"Gruber","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alan 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