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…

One of the important underlying assumptions of all item response theory (IRT) models is that of local independence. This assumption requires that the response to an item on a test not be influenced by the response to any other items. This assumption is often taken for granted, with little or no scrutiny of the response process required to answer…

Three Autoregressive Integrated Moving Averages (ARIMA) forecast procedures for Census Bureau X-11 concurrent seasonal adjustment were empirically tested. Forty time series from three Census Bureau economic divisions (business, construction, and industry) were analyzed. Forecasts were obtained from fitted seasonal ARIMA models augmented with…

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…

In research, data sets often occur in which the variance of the distribution of the dependent variable at given levels of the predictors is a function of the values of the predictors. In this situation, the use of weighted least-squares (WLS) or techniques is required. Weights suitable for use in a WLS regression analysis must be estimated. A…

This paper reviews recent work in factor analysis of categorical variables. Emphasis is on the generalized least squares solution. A section on maximum likelihood solution focuses on extensions of the classical model, especially the normal case. Many of the recent developments have taken place within this context, and it provides a unified…

In this paper, the detection of response patterns aberrant from the Rasch model is considered. For this purpose, a new person fit index, recently developed by I. W. Molenaar (1987) and an iterative estimation procedure are used in a simulation study of Rasch model data mixed with aberrant data. Three kinds of aberrant response behavior are…

The Rasch Model and various extensions of this model can be formulated as a quasi loglinear model for the incomplete subgroup x score x item response 1 x ... x item response k contingency table. By comparing various loglinear models, specific deviations of the Rasch model can be tested. Parameter estimates can be computed using programs such as…

J. A. Emrick's (1971) model is a latent class model of mastery testing that can be used to estimate the proportion of masters in a given population. A. Hamerle (1980), in a recent paper on this model, has proposed an estimator for the proportion of masters that is claimed to constitute a maximum likelihood approach. It is indicated that Hamerle is…

This study developed a hybrid of item response theory (IRT) models and latent class models, which combined the strengths of each type of model. The primary motivation for developing the new model is to describe characteristics of examinees' knowledge at the time of the examination. Hence, the application of the model lies mainly in so-called…

Two optimalization models for the construction of tests with a maximal value of coefficient alpha are given. Both models have a linear form and can be solved by using a branch-and-bound algorithm. The first model assumes an item bank calibrated under the Rasch model and can be used, for instance, when classical test theory has to serve as an…

In the last decade, a modeling technique has been developed to handle complex input/output analyses where outputs involve joint products and there are no known mathematical relationships linking the outputs or inputs. The technique uses the geometrical concept of a six-dimensional shape called a polytope to analyze the efficiency of each…

This report describes new statistical procedures for item response analysis using estimation of item response curves used in mental testing with ability parameters treated as a random sample. Modern computer technology and the EM algorithm make this solution possible. The research focused on the theoretical formulation and solution of maximum…

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…