This paper suggests several item selection criteria for adaptive testing that are all based on the use of the true posterior. Some of the ability estimators produced by these criteria are discussed and empirically criticized. (SLD)

A new estimation method, Weighted Likelihood Estimation (WLE), is derived mathematically. Two Monte Carlo studies compare WLE with maximum likelihood estimation and Bayesian modal estimation of ability in conventional tests and tailored tests. Advantages of WLE are discussed. (SLD)

Information functions are used to find the optimum ability levels and maximum contributions to information for estimating item parameters in three commonly used logistic item response models. Implications are discussed for applications such as adaptive testing and test construction. (SLD)

Two simple empirical approximate Bayes estimators are introduced for estimating domain scores under binomial and hypergeometric distributions respectively. Criteria are established regarding use of these functions over maximum likelihood estimation counterparts. (SLD)

Using the constant information model, constant amounts of test information, and a finite interval of ability, simulated data were produced for 8 ability levels and 20 numbers of test items. Analyses suggest that it is desirable to consider modifying test information functions when they measure accuracy in ability estimation. (SLD)

Replenishing item pools for on-line ability testing requires innovative and efficient data collection. A method is proposed to collect test item calibration data in an on-line testing environment sequentially using locally D-optimum designs, thereby achieving high Fisher information for the item parameters. (SLD)