Analyzing small psychological experiments
with item response models
Richard J. Patz, Brian W. Junker, F. Javier Lerch and Brian
For discrete repeated measures data, item response theory (IRT) models and Rasch-type models
in particular provide a direct way to model within-subjects dependence.
Experimental repeated measures data, commonly gathered by psychologists
and educational researchers, exhibit within-subjects
dependence, and yet sample sizes are often too small to allow stable fitting
using standard IRT programs.
In this paper we discuss the application of IRT models in this small-scale
experimental context. We show that when attention is focused on a small number
of hypotheses, IRT models may be adapted to evaluate the
hypotheses while accounting for within-subjects, between-measures
dependence. We illustrate our approach by analyzing polytomous
response data from a small experiment in cognitive psychology that examines
the stresses that telephone-based menu systems place on human working memory.
We develop a polytomous Rasch model, and we generalize Rigdon and
Tsutakawa's (1983) E-M algorithm along the lines of Glas and Verhelst (1989)
to obtain a stable model fit. We discuss hypothesis evaluation and
important sensitivity issues, and we compare different strategies for
efficient numerical computation.
Index terms: cognitive psychology, computational issues, E-M algorithm,
item response models, maximum likelihood, polytomous response data,
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