Pretest Item Analyses Using Polynomial Logistic Regression : An Approach to Small Sample Calibration Problems Associated with Computerized Adaptive Testing / Liane N. Patsula and Peter J. Pashley.

Many large-scale testing programs routinely pretest new items alongside operational (or scored) items to determine their empirical characteristics. If these pretest items pass certain statistical criteria, they are placed into an operational item pool; otherwise they are edited and re-pretested or simply discarded. In these situations, reliable ability estimates are usually available for each examinee based on operational items, and they may be treated as fixed. If so, polynomial (in ability, theta) logistic regression analyses can be conducted using a variety of statistical software packages. In this study, a cubic logistic model (theta, theta-2, theta-3) was found to fit standard three-parameter (i.e. discrimination, difficulty, and lower asymptote) logistic item response theory (IRT) model items very well. When employing a polynomial logistic model, well-known selection routines (such as stepwise elimination) can be utilized to reduce the number of required parameters for certain items, thus reducing the sample sizes needed for reliable estimation. With this model, simultaneous confidence bands are easily calculated. As an added benefit, given that a polynomial logistic function is not necessarily monotonically increasing with ability, poor quality items and incorrect alternative responses can also be fit using the same estimation procedures. (Contains 19 figures, 4 tables, and 22 references.) (Author/SLD)

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