Graphical analysis of item response theory residuals

Abstract

A graphical comparison of empirical versus simulated residual variation is presented as one way to assess the goodness of fit of an item response theory model. The two forms of residual variation were generated through the separate calibration of empirical data and data "tailored" to fit the model, given the empirical parameter estimates. A variety of techniques illustrate the utility of using tailored residuals as a specific baseline against which empirical residuals may be understood. This paper presents an analytic method for isolating and identifying departures from the fit of an item response theory (IRT) model. The specific techniques employed focus on the graphical comparison of empirical residual variation to baseline residual variation. The baseline variation is the result of data generated to fit the model, given the empirical parameter estimates. The baseline residuals thus serve as the reference background for interpreting the empirical residuals. Although the Rasch model is applied in this paper, the principles that are discussed and illustrated hold for the residual analysis of any IRT model.