The Analysis of Item-Ability Regressions: An Exploratory IRT Model Fit Tool

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Abstract
The use of item-ability regressions (the comparison of the regression of the observed proportion of people answering an item correctly on estimated θ with the estimated item response function) to investigate the psychometric properties of particular item types in a given population was explored using data from four administrations of 10 item types (a total of 806 items) from the Graduate Record Examinations General Test. Although the method does not allow an absolute deter mination of fit for a latent trait model (in this case, for the three-parameter logistic model), it does show that certain item types consistently fit the model worse than other item types, and it led to and supported a specific hypothesis as to why the model probably did not fit these item types.