Diagnostics for Influential Data in IRT (Item Response Theory) Scoring.
ADVANCED STATISTICAL TECHNOLOGIES CORP LAWRENCEVILLE NJ
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Within the context of item response theory, this paper explores a class of statistics for detecting unusual, aberrant response patterns. These statistics are based on regression diagnostics for detecting influential data. They are derived by linearizing the maximum likelihood estimator to show that it is, approximately, a linear combination of the components of the response vector then standard linear regression diagnostics formulas Belsley, Kuh Welsch, 1980 are applied in the same way used in Pregibon 1981. This paper uses the Fletcher-Marquart-Levenberg extension to the Gauss-Newton algorithm to linearize the MLE. This approach is different from that of Pregibon 1981 which used the Newton-Raphson algorithm. This approach enables regression diagnostics for a wider class of nonlinear models than considered in Pregibon 1981 Pregibons models were limited to logistic regression and other generalized linear models McCullagh Nelder, 1983. This papers class of models includes all models which have differentials with respect to the parameters it includes the three parameter logistic item response models Lord, 1980. As an example application, the diagnostic statistics were used to study the item response model of Drasgow Levine 1985, which models cheating or deliberate-failure behavior. This study shows that the diagnostics can be used for appropriateness measurement.
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