The effects of using a unidimensional item response theory (IRT) model were compared with two-dimensional data generated by non-compensatory and compensatory multidimensional IRT models. The number-correct distributions for each dataset group were comparable, although factor analyses of tetrachoric correlations suggested differences in data…

The fundamental mathematical model of L. L. Thurstone's common factor analysis is reviewed, and basic covariance matrices of maximum likelihood factor analysis and alpha factor analysis are presented. The methods are compared in terms of computational and scaling contrasts. Weighting and the appropriate number of common factors are considered.…

In this article, an overview of nonparametric item response theory methods for determining the dimensionality of item response data is provided. Four methods were considered: MSP, DETECT, HCA/CCPROX, and DIMTEST. First, the methods were compared theoretically. Second, a simulation study was done to compare the effectiveness of MSP, DETECT, and…

Three heuristic methods of assessing the dimensionality of binary item pools were evaluated in a Monte Carlo investigation. The indices were based on (1) the local independence of unidimensional tests; (2) patterns of second-factor loadings derived from simplex theory; and (3) the shape of the curve of successive eigenvalues. (SLD)

Geometric approaches to representing interrelations among tests and items are compared with an additive tree model (ATM), using 2,644 examinees and 2 other data sets. The ATM's close fit to the data and its coherence of presentation indicate that it is the best means of representing tests and items. (TJH)

A mathematical model is proposed to describe how group differences in distributions of abilities, which are distinct from the target ability, influence the probability of a correct item response. In the multidimensional approach, differential item functioning is considered a function of the educational histories of the examinees. (SLD)

The similarity of information provided by direct and indirect methods of writing assessment was investigated using 219 tenth graders. A resulting cognitive model of writing skills indicates that practitioners interested in reliably measuring all aspects of the proposed writing process continuum use both direct and indirect methods. (TJH)