Estimating parameters of dichotomous and ordinal item response models with gllamm
Xiaohui Zheng
Graduate School of Education
University of California, Berkeley
Berkeley, CA
[email protected]
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Sophia Rabe-Hesketh
Graduate School of Education
University of California, Berkeley
Berkeley, CA
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Abstract. Item response theory models are measurement models for categorical
responses. Traditionally, the models are used in educational testing, where
responses to test items can be viewed as indirect measures of latent
ability. The test items are scored either dichotomously
(correct–incorrect) or by using an ordinal scale (a grade from poor to
excellent). Item response models also apply equally for measurement of other
latent traits. Here we describe the one- and two-parameter logit models for
dichotomous items, the partial-credit and rating scale models for ordinal
items, and an extension of these models where the latent variable is
regressed on explanatory variables. We show how these models can be
expressed as generalized linear latent and mixed models and fitted by using
the user-written command gllamm.
View all articles by these authors:
Xiaohui Zheng, Sophia Rabe-Hesketh
View all articles with these keywords:
gllamm, gllapred, latent variables, Rasch model, partial-credit model, rating scale model, latent regression, generalized linear latent and mixed model, adaptive quadrature, item response theory
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