Journal
MULTIVARIATE BEHAVIORAL RESEARCH
Volume 52, Issue 4, Pages 465-484Publisher
ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD
DOI: 10.1080/00273171.2017.1309262
Keywords
Bifactor model; diagnostic classification model; item response theory; minimum description length; model evaluation
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Funding
- Institute of Education Sciences [R305D140046]
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Complexity in item response theory (IRT) has traditionally been quantified by simply counting the number of freely estimated parameters in the model. However, complexity is also contingent upon the functional form of the model. We examined four popular IRT models-exploratory factor analytic, bifactor, DINA, and DINO-with different functional forms but the same number of free parameters. In comparison, a simpler (unidimensional 3PL) model was specified such that it had 1 more parameter than the previous models. All models were then evaluated according to the minimum description length principle. Specifically, each model was fit to 1,000 data sets that were randomly and uniformly sampled from the complete data space and then assessed using global and item-level fit and diagnostic measures. The findings revealed that the factor analytic and bifactor models possess a strong tendency to fit any possible data. The unidimensional 3PL model displayed minimal fitting propensity, despite the fact that it included an additional free parameter. The DINA and DINO models did not demonstrate a proclivity to fit any possible data, but they did fit well to distinct data patterns. Applied researchers and psychometricians should therefore consider functional form-and not goodness-of-fit alone-when selecting an IRT model.
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