As examples of models that are not based on normality or its approximation, the logistic positive exponent family of models is discussed. These models include the item task complexity as the third parameter, which determines the single principle of ordering individuals on the ability scale. (SLD)

Discusses whether the tradition of accepting point-symmetric item characteristic curves is justified by uncovering the inconsistent relationship between the difficulties of items and the order of maximum likelihood estimates of ability. In this context, proposes a family of models, called the logistic positive exponent family, that provides…

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…

A new model, the acceleration model, is proposed in the framework of the heterogeneous case of the graded response model, based on processing functions defined for a finite or enumerable number of steps. The model is expected to be useful in cognitive assessment. (SLD)

Introduces and discusses the rationale and procedures of two nonparametric approaches to estimating the operating characteristic of a discrete item response, or the conditional probability, given the latent trait, that the examinee's response be that specific response. (SLD)

Latent trait models introduced the concept of the latent trait, or ability, as distinct from the test score. There is a recent tendency to treat the test score as through it were a substitute for ability, largely because the test score is a convenient way to place individuals in order. F. Samejima (1969) has shown that, in general, the amount of…

F. Samejima's approximation for the bias function for the maximum likelihood estimate of the latent trait in the general case where item responses are discrete is explored. Observations are made about the behavior of this bias function for the dichotomous response level in general. Empirical examples are given. (SLD)

An approximation for the bias function of the maximum likelihood estimate of the latent trait or ability is developed for the general case where item responses are discrete, which includes the dichotomous response level, the graded response level, and the nominal response level. (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)

The accuracy of estimation of the subjects' latent ability maintained by tailoring for each testee the order of item presentation and the border of item dichotomization was compared to the information provided by the original graded test items. (RC)