The Person Response Curve: Fit of Individuals to Item Characteristic Curve Models

Abstract
This study investigated a method of determining the fit of individuals to item characteristic curve (ICC) models using the person response curve (PRC). The construction of observed PRCs is based on an individual's proportion correct on test item subsets (strata) that differ systematically in difficulty level. A method is proposed for identifying irregularities in an observed PRC by comparing it with the expected PRC predicted by the three- parameter ICC logistic model for that individual's ability level. Diagnostic potential of the PRC is discussed in terms of the degree and type of deviations of the observed PRC from the expected PRC predicted by the model. Observed PRCs were constructed for 151 college students using vocabulary test data on 216 items of wide difficulty range. Data on student's test-taking motivation, test- taking anxiety, and perceived test difficulty were also obtained. PRCs for the students were found to be reliable an to have shapes that were primarily a function of ability level. Three-parameter logistic (ICC) model expected PRCs served as good predictors of observed PRCs for over 90% of the group. As anticipated from this general overall fit of the observed data to the ICC model, there were no significant correlations between degree of non-fit and test-taking motivation, test-taking anxiety, or perceived test difficulty. Using split-pool observed PRCs, a few students were identified who deviated significantly from the expected PRC.

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