In this study, psychometric properties of the test of the three-mathematical minds (M3) were investigated. The M3 test was developed based on a multidimensional conception of giftedness to identify mathematically talented students. Participants included 291 middle-school students. Data analysis indicated that the M3 had a 0.73 coefficient as a…

Computerized adaptive testing is subject to security problems, as the item bank content remains operative over long periods and administration time is flexible for examinees. Spreading the content of a part of the item bank could lead to an overestimation of the examinees' trait level. The most common way of reducing this risk is to impose a…

A rating response mechanism for ordered categories such as in Likert scaling, which is related to the traditional threshold formulation but distinctively different from it, is formulated. The mechanism is based on the Rasch model. Two parameters in addition to the usual Rasch parameters are identified and discussed. (Author/JKS)

Deciding whether sets of test data are consistent with any of a large class of item response models is considered. The assumption of local independence is weakened to a new condition, local nonnegative dependence (LND). Necessary and sufficient conditions are derived for a LND item response model. (Author/JKS)

When the parameters of item response data are estimated by a latent trait model, some variation will remain unaccounted. If baseline graphical configurations of the residual variation can be constructed, measurement irregularities may be exposed. An analytic strategy for the graphical representation and analysis of Rasch model residuals is…

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)…

Although it has been claimed that the Rasch model leads to a higher degree of objectivity in measurement than has been previously possible, this model has had little impact on test development. Population-invariant item and ability calibrations along with the statistical equivalency of any two item subsets are supposedly possible if the item pool…

An approximate relationship is devised between the unidimensional model used in data analysis and a multidimensional model hypothesized to be generating the item responses. Scale shrinkage is successfully predicted for several sets of simulated data. (Author/LMO)

The relationship between item parameter values obtained from independent Birnbaum (l968) model calibrations of the same item set from two different samples is examined. (Author)

Social and naturally occurring choice phenomena are often of the "pick any" type in which the number of choices made by a subject as well as the set of alternatives from which they are chosen is unconstrained. A model and scaling method for these data are introduced. (Author/JKS)

A class of multidimensional latent trait models is described. The properties of the model parameters, and initial results on the accuracy of a maximum likelihood procedure for estimating the model parameters are discussed. The model presented is a special case of the general model described by Rasch (1961), with close similarities to the models…

A scaling technique known as the Method of Reciprocal Averages has been in use since the early 1930's. This technique yields a set of item response weights for a psychological inventory which maximizes the internal consistency of the inventory for a group of subjects. Although the technique has been used for many years, its mathematical…

It is shown that empirical mental test P - P plots are approximately equal to theoretical item-item curves, at least for long tests administered to many people. This result is important because it leads to (1) a distribution free method for estimating points on item-item curves; (2) a general method for defining estimates of item parameters; and…

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…

Several special cases of the general Rasch model, varying in complexity, were investigated to determine whether they could successfully model realistic multidimensional item response data. Whether the parameters of the model could be readily interpreted was also investigated. The models investigated included: (1) the vector model; (2) the product…