Diagnostics for Influential Data in IRT (Item Response Theory) Scoring.
Abstract
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); Pregibon's models were limited to logistic regression and other generalized linear models (McCullagh & Nelder, 1983). This paper's 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1986
- Accession Number
- ADA179120
Entities
People
- Douglas H. Jones