Samejima ("Psychometrika "65:319--335, 2000) proposed the logistic positive exponent family of models (LPEF) for dichotomous responses in the unidimensional latent space. The objective of the present paper is to propose and discuss a graded response model that is expanded from the LPEF, in the context of item response theory (IRT). This…

This paper describes the graded response model. The graded response model represents a family of mathematical models that deal with ordered polytomous categories, such as: (1) letter grading; (2) an attitude survey with "strongly disagree, disagree, agree, and strongly agree" choices; (3) partial credit given in accord with an…

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)

The rationale behind the method of estimating the operating characteristics of discrete item responses when the test information of the Old Test is not constant was presented previously. In the present study, two subtests of the Old Test, i.e. Subtests 1, and 2, each of which has a different non-constant test information function, are used in…

In line with the latent trait model, the continuous response level is defined and considered, in contrast to the discrete response levels, which have already been explored by the author. (Editor)

The three-parameter logistic model by Birnbaum for the multiple-choice item in the latent trait theory is considered with respect to the item response information function and the unique maximum condition. (Editor/RK)

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…

Traditionally, the test score represented by the number of items answered correctly was taken as an indicator of the examinee's ability level. Researchers still tend to think that the number-correct score is a way of ordering individuals with respect to the latent trait. The objective of this study is to depict the benefits of using ability…

A general model for the homogeneous case of the continuous response is proposed. The model is an expansion and generalization of the one proposed by the author in 1974, in which the open response situation is dealt with. In this generalized model, the closed response situation is dealt with, and it includes the model for the open response…

The logistic positive exponent family (LPEF) of models has been proposed by F. Samejima (1998) for dichotomous responses. This family of models is characterized by point-asymmetric item characteristic curves (ICCs). This paper introduces the LPEF family, and discusses its usefulness in educational measurement and the implications of its use.…

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.…

This paper proposes a general model for free-response data collected for measuring a specified unidimensional psychological process; systematizes situations which vary with respect to the scoring level of items; and finds out general conditions for the operating characteristic of an item response category to provide a unique maximum likelihood…

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)

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…