Recent advances in data recording technology have given researchers new ways of collecting on-line and continuous data for analyzing input-output systems. For example, continuous response digital interfaces are increasingly used in psychophysics. The statistical problem related to these input-output systems reduces to linking time-varying…

The models and procedures discussed in this paper are related to those presented in Bock and Aitkin (1981), where they considered the 2-parameter probit model and approximated a normally distributed prior distribution of abilities by a finite and discrete distribution. One purpose of this paper is to clarify the nature of the general EM (GEM)…

One means of learning about the processes operating in a multiple choice test is to include some test items, called nonsense items, which have no correct answer. This paper compares two versions of a mathematical model of test performance to interpret test data that includes both genuine and nonsense items. One formula is based on the usual…

Significant to a latent trait or item response theory analysis of a mental test is the determination of exactly what is being quantified. The following are practical problems to be considered in the formulation of a good theory: (1) deciding whether two tests measure the same trait or traits; (2) analyzing the relative contributions of a pair of…

This paper reviews the existing multidimensional item response theory (IRT) models and demonstrates how one of the models can be applied to estimation of abilities from a test measuring more than one dimension. The purposes of this paper were threefold. First, the fundamental concepts required when considering multidimensional models for the…

This paper briefly demonstrates a few of the possibilities of a systematic application of robustness theory, concentrating on the estimation of ability when the true item response model does and does not fit the data. The definition of the maximum likelihood estimator (MLE) of ability is briefly reviewed. After introducing the notion of…

This paper provides an up-to-date review of the relationship between item response theory (IRT) and (nonlinear) common factor theory and draws out of this relationship some implications for current and future research in IRT. Nonlinear common factor analysis yields a natural embodiment of the weak principle of local independence in appropriate…

Psychometric theory has been one of psychology's stronger foundations and a major contributor to the recognition of psychology as a scientific discipline. Basic principles of psychometric theory led to the development of respected intelligence tests and large and comprehensive testing and assessment programs. This paper synthesizes major…

The effects of a multidimensional latent trait space on estimation of item and person parameters by the computer program LOGIST are examined. Several item pools were simulated that ranged from truly unidimensional to an inconsequential general latent trait. Item pools with intermediate levels of prepotency of the general latent trait were also…

Recent developments in dichotomous factor analysis based on multidimensional item response models (Bock and Aitkin, 1981; Muthen, 1978) provide an effective method for exploring the dimensionality of questionnaire items. Implemented in the TESTFACT program, this "full information" item factor analysis accounts not only for the pairwise…

A primary goal of this study was to determine the extent to which item difficulty was related to item position and, if a significant relationship was found, to suggest adjustments to predicted item difficulty that reflect differences in item position. Item response data from the Medical College Admission Test (MCAT) were analyzed. A data set was…

A Monte Carlo study of five indices of dimensionality of binary items used a computer model that allowed sampling of both items and people. Five parameters were systematically varied in a factorial design: (1) number of common factors from one to five; (2) number of items, including 20, 30, 40, and 60; (3) sample sizes of 125 and 500; (4) nearly…

This paper demonstrates the relationship between the concept of unidimensionality and direction of an item in a multidimensional space. The basic premise is that if items that measure in the same direction are combined to form a test, that test will meet the item response theory requirements of unidimensionality. This will be true even if the…

This report contains the Proceedings of the 1982 Item Response Theory and Computerized Adaptive Testing Conference. The papers and their discussions are organized into eight sessions: (1) "Developments in Latent Trait Theory," with papers by Fumiko Samejima and Michael V. Levine; (2) "Parameter Estimation," with papers by…