Abstract
In psychometric practice, the parameter estimates of a standard item-response theory (IRT) model can become biased when item-response data, of persons' individual responses to test items, contain outliers relative to the model. Also, the manual removal of outliers can be a time-consuming and difficult task. Besides, removing outliers leads to data information loss in parameter estimation. To address these concerns, a Bayesian IRT model that includes person and latent item-response outlier parameters, in addition to person ability and item parameters, is proposed and illustrated, and is defined by item characteristic curves (ICCs) that are each specified by a robust, Student's t-distribution function. The outlier parameters and the robust ICCs enable the model to automatically identify item-response outliers, and to make estimates of the person ability and item parameters more robust to outliers. Hence, under this IRT model, it is unnecessary to remove outliers from the data analysis. Our IRT model is illustrated through the analysis of two data sets, involving dichotomous- and polytomous-response items, respectively.
Highlights
Item-response theory (IRT) models are often used for the analysis of item-response data, consisting of persons’ individual responses to a set of test items
Standard IRT models assume that the likelihood of a correct item response is a logistic function of person ability and item parameters (e.g., Embretson & Reise, 2000)
Among the 3,000 total item responses in the National Assessment of Educational Progress (NAEP) data set, the IRT model in this study indicated that 77 of them were item-response outliers, with marginal posterior probability estimated as Pr.1=2
Summary
Item-response theory (IRT) models are often used for the analysis of item-response data, consisting of persons’ individual responses to a set of test items (e.g., exam or survey). This model automatically identifies item-response outliers using MCMC, and downweights outliers (through latent error variance inflation) to provide posterior estimation of person and item parameters that is more robust to outliers.
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