Item response theory (IRT) has been adapted as the theoretical foundation of computerized adaptive testing (CAT) for several decades. In applying IRT to CAT, there are certain considerations that are essential, and yet tend to be neglected. These essential issues are addressed in this paper, and then several ways of eliminating noise and bias in…

The reliability coefficient is predicted from the test information function (TIF) or two modified TIF formulas and a specific trait distribution. Examples illustrate the variability of the reliability coefficient across different trait distributions, and results are compared with empirical reliability coefficients. (SLD)

The methods and approaches for estimating the operating characteristics of the discrete item responses without assuming any mathematical form have been developed and expanded. It has been made possible that, even if the test information function of a given test is not constant for the interval of ability of interest, it is used as the Old Test.…

Some cognitive psychologists, who have tried to approach psychometric theories, say that the psychometric approach does not provide them with theories and methods with which they can deal with differential strategies. In this paper, a general latent trait model for differential strategies in cognitive processes is proposed which includes three…

In defense of retaining the "latent trait theory" term, instead of replacing it with "item response theory" as some recent research would have it, the following objectives are outlined: (1) investigation of theory and method for estimating the operating characteristics of discrete item responses using a minimum number of…

In the methods and approaches developed for estimating the operating characteristics of the discrete item responses, the maximum likelihood estimate of the examinee based upon the "Old Test" has an important role. When Old Test does not provide a sufficient amount of test information for the upper and lower part of the ability interval,…

Several important implications in latent trait theory, with implications for individualized or tailored testing, are pointed out. A way of using the information function in tailored testing in connection with the standard error estimation of the ability level using maximum likelihood estimation is suggested. (Author/JKS)

Test validity is a concept that has often been ignored in the context of latent trait models and in modern test theory, particularly as it relates to computerized adaptive testing. Some considerations about the validity of a test and of a single item are proposed. This paper focuses on measures that are population-free and that will provide local…

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)

A method is proposed that increases the accuracies of estimation of the operating characteristics of discrete item responses, especially when the true operating characteristic is represented by a steep curve, and also at the lower and upper ends of the ability distribution where the estimation tends to be inaccurate because of the smaller number…

Because of the recent popularity of the three-parameter logistic model among the researchers who apply latent trait theory, it will be worthwhile to investigate the effect of noise accommodated in different models. In the present paper, four types of models on the dichotomous response level, Types A, B, C and D, are considered. Type A does not…

A method of estimating the operating characteristics of a new test item added to an established test without assuming a prior model has been proposed by the author. In this paper, the author extends this logic by proposing a different hypothesized distribution of the resulting estimate. The former method used a normal approximation; the present…

Simple sum procedure of the conditional PDF approach (plausiblity of distractor function) combined with the normal approach method was applied for estimating the plausibility functions of the distractors of the Level II vocabulary subtest items of the Iowa Tests of Basic Skills. In so doing, the normal ogive model was adopted for the correct…

Two modification formulas are presented for the test information function in order to provide better measures of local accuracies of the estimation of "theta" when maximum likelihood estimation is used to provide the estimate of ability "theta." A minimum bound of any estimator, biased or unbiased, is considered; and Formula 1…

This paper is the final report of a multi-year project sponsored by the Office of Naval Research (ONR) in 1987 through 1990. The main objectives of the research summarized were to: investigate the non-parametric approach to the estimation of the operating characteristics of discrete item responses; revise and strengthen the package computer…