Author: Revuelta, Javier¹

Source: British Journal of Mathematical and Statistical Psychology, Volume 61, Number 1, May 2008 , pp. 93-113(21)

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• In this Subject: Mathematics and Statistics ,  Psychology
• By this author: Revuelta, Javier

Abstract:

Testing the fit of finite mixture models is a difficult task, since asymptotic results on the distribution of likelihood ratio statistics do not hold; for this reason, alternative statistics are needed. This paper applies the π* goodness of fit statistic to finite mixture item response models. The π* statistic assumes that the population is composed of two subpopulations - those that follow a parametric model and a residual group outside the model; π* is defined as the proportion of population in the residual group. The population was divided into two or more groups, or classes. Several groups followed an item response model and there was also a residual group. The paper presents maximum likelihood algorithms for estimating item parameters, the probabilities of the groups and π*. The paper also includes a simulation study on goodness of recovery for the two- and three-parameter logistic models and an example with real data from a multiple choice test.

Document Type: Research article

DOI: 10.1348/000711006X136843

Affiliations: 1: Department of Social Psychology and Methodology, Autónoma University of Madrid, Spain

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