The purpose of this article is to present logistic discriminant function analysis as a means of differential item functioning (DIF) identification of items that are polytomously scored. The procedure is presented with examples of a DIF analysis using items from a 27‐item mathematics test which includes six open‐ended response items scored polytomously. The results show that the logistic discriminant function procedure is ideally suited for DIF identification on nondichotomously scored test items. It is simpler and more practical than polytomous extensions of the logistic regression DIF procedure and appears to fee more powerful than a generalized Mantel‐Haenszelprocedure.

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The purpose of this article is to present an analytical derivation for the mathematical form of an average between-test overlap index as a fitnction of the item exposure index, for fixed-length computerized aahptive tests (CATs). This algebraic relationship is used to investigate the simultaneous control of item exposure at both the item and test levels. The results indicate that, in jixed-length CATs, control of the average between-test overlap is achieved via the mean and variance of the item exposure rates of the items that constitute the CAT item pool. The mean of the item exposure rates is easily manipulated Control over the variance of the item exposure rates can be achieved via the maximum item exposure rate (r-).Therefore, item exposure control methods which implement a specification of r, , (e.g., Sympson & Hetter;1985) provide the most direct control at both the item and test levels.

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