The predictive analysis approach to adaptive testing originated in the idea of statistical predictive analysis suggested by J. Aitchison and I.R. Dunsmore (1975). The adaptive testing model proposed is based on parameter-free predictive distribution. Aitchison and Dunsmore define statistical prediction analysis as the use of data obtained from an…

In most item response theory models a particular mathematical form is assumed for all item characteristic curves, e.g., a logistic function. It could be desirable, however, to estimate the shape of the item characteristic curves without prior restrictive assumptions about its mathematical form. We have developed a practical method of estimating…

Many combinations of a method and an approach for estimating the operating characteristics of the graded item responses, without assuming any mathematical forms, have been produced. In these methods, a set of items whose characteristics are known, or Old Test, is used, which has a large, constant amount of test information throughout the interval…

The application of latent trait theory to classroom tests necessitates the use of small sample sizes for parameter estimation. Computer generated data were used to assess the accuracy of estimation of the slope and location parameters in the two parameter logistic model with fixed abilities and varying small sample sizes. The maximum likelihood…

The purpose of this study was to compare and evaluate five online pretest item calibration/scaling methods in computerized adaptive testing (CAT): (1) the marginal maximum likelihood estimate with one-EM cycle (OEM); (2) the marginal maximum likelihood estimate with multiple EM cycles (MEM); (3) Stocking's Method A (M. Stocking, 1988); (4)…

The sensitivity of marginal maximum likelihood estimation of item and ability (theta) parameters was examined when prior ability distributions were not matched to underlying ability distributions. Thirty sets of 45-item test data were generated. Conditions affecting the accuracy of estimation are discussed. (SLD)

A method for incorporating maximum likelihood (ML) estimation into reliability analyses with item-level missing data is outlined. An ML estimate of the covariance matrix is first obtained using the expectation maximization (EM) algorithm, and coefficient alpha is subsequently computed using standard formulae. A simulation study demonstrated that…

An extension of the Bock-Samejima model for multiple choice items is introduced. The model provides for varying probabilities of the response alternative when the examinee guesses. A marginal maximum likelihood method is devised for estimating the item parameters, and likelihood ratio tests for comparing more and less constrained forms of the…

In a preceding research report, ONR/RR-82-1 (Information Loss Caused by Noise in Models for Dichotomous Items), observations were made on the effect of noise accommodated in different types of models on the dichotomous response level. In the present paper, focus is put upon the three-parameter logistic model, which is widely used among…

Computerized adaptive testing procedures (CATPs) based on the graded response method (GRM) of F. Samejima (1969) and the partial credit model (PCM) of G. Masters (1982) were developed and compared. Both programs used maximum likelihood estimation of ability, and item selection was conducted on the basis of information. Two simulated data sets, one…

A method for determining invariant item parameters is presented, along with a scheme for obtaining test scores which are interpretable in terms of a common metric. The method assumes a unidimensional latent trait and uses a three parameter normal ogive model. The assumptions of the model are explored, and the methods for calculating the proposed…

This is a continuation of a previous study in which a new method of estimating the operating characteristics of discrete item responses based upon an Old Test, which has a non-constant test information function, was tested upon each of two subtests of the original Old Test, Subtests 1 and 2. The results turned out to be quite successful. In the…

Assuming vectors of item responses depend on ability through a fully specified item response model, this paper presents maximum likelihood equations for estimating the population parameters without estimating an ability parameter for each subject. Asymptotic standard errors, tests of fit, computing approximations, and details of four special cases…

An extension is proposed for the network algorithm introduced by C.R. Mehta and N.R. Patel to construct exact tail probabilities for testing the general hypothesis that item responses are distributed according to the Rasch model. A simulation study indicates the efficiency of the algorithm. (SLD)

A loglinear item response theory (IRT) model is proposed that relates polytomously scored item responses to a multidimensional latent space. The analyst may specify a response function for each response, and each item may have a different number of response categories. Conditional maximum likelihood estimates are derived. (SLD)