A Nonparametric Approach for Assessing Goodness-of-Fit of IRT Models in a Mixed Format Test
APPLIED MEASUREMENT IN EDUCATION(2015)
Abstract
Investigating the fit of a parametric model plays a vital role in validating an item response theory (IRT) model. An area that has received little attention is the assessment of multiple IRT models used in a mixed-format test. The present study extends the nonparametric approach, proposed by Douglas and Cohen (2001), to assess model fit of three IRT models (three- and two-parameter logistic model, and generalized partial credit model) used in a mixed-format test. The statistical properties of the proposed fit statistic were examined and compared to S-X-2 and PARSCALE's G(2). Overall, RISE (Root Integrated Square Error) outperformed the other two fit statistics under the studied conditions in that the Type I error rate was not inflated and the power was acceptable. A further advantage of the nonparametric approach is that it provides a convenient graphical inspection of the misfit.
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Key words
monte carlo methods,nonparametric statistics,goodness of fit,item response theory,comparative analysis
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