Fitting IRT models to dichotomous and polytomous data: Assessing the relative model-data fit of ideal point and dominance models

Louis Tay, Usama S. Ali, Fritz Drasgow, Bruce Williams

Research output: Contribution to journalArticlepeer-review

Abstract

This study investigated the relative model-data fit of an ideal point item response theory (IRT) model (the generalized graded unfolding model [GGUM]) and dominance IRT models (e.g., the two-parameter logistic model [2PLM] and Samejima's graded response model [GRM]) to simulated dichotomous and polytomous data generated from each of these models. The relative magnitudes of the adjusted χ2/df ratios for item pairs and item triples at the test level were used to evaluate fit. Two simulation studies were conducted, one for dichotomous data and the other for polytomous data. Relative fit of the ideal point and dominance models were compared with respect to different conditions: test length, sample size, and sample type. In many simulated conditions, it was found that comparing relative fits (using test-level doubles and triples adjusted χ2/df ratios) almost always consistently pointed to the correct IRT model. However, GGUM could fit dichotomous two-parameter logistic (2PL) data well when the scale length was short (i.e., 15 items); nevertheless, an examination of estimated GGUM item parameters clearly shows dominance item characteristics. Results of the simulation studies and implications are discussed.

Original languageEnglish (US)
Pages (from-to)280-295
Number of pages16
JournalApplied Psychological Measurement
Volume35
Issue number4
DOIs
StatePublished - Jun 2011

Keywords

  • IRT model fit
  • attitude measurement
  • dominance models
  • ideal point models
  • item response theory
  • simulation
  • unfolding

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Psychology (miscellaneous)

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