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A logistic mixture distribution model for polychotomous item responses
Author(s) -
Rost Jürgen
Publication year - 1991
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1991.tb00951.x
Subject(s) - rasch model , generalization , inference , latent class model , class (philosophy) , mathematics , statistics , computer science , mixture model , econometrics , artificial intelligence , mathematical analysis
The polychotomous Rasch model is generalized to a mixture distribution model. It is assumed that the observed data are generated by two or more latent classes of individuals so that within each class the polychotomous Rasch model holds but with different parameters between the classes. Hence, the proposed model is also a generalization of latent class analysis which allows for quantitative individual differences within the classes. A parameter estimation procedure is outlined, employing conditional inference methods for the item parameters within classes and the EM‐algorithm for unmixing the data. The application of the model and control of model fit are illustrated by means of real data and simulated data.