The Influence of Multidimensionality on the Graded Response Model

Abstract

Most item response theory models assume a uni-dimensional latent space. This study extended previous work on the effects of dimensionality on parameter estimation for dichotomous models to the polytomous graded response model. A multidimensional graded response model was developed to generate data in one, two, and three dimensions. The two- and three-dimension conditions contained datasets that varied in their interdimensional association. The effects of test length and the ratio of sample size to the number of item parameters estimated also were investigated. For the unidimensional data, a sample size ratio of 5:1 provided reasonably accurate estimation; increasing test length from 15 to 30 items did not have a significant impact on the accuracy of item parameter estimation. Regardless of the dimensionality of the data, the difficulty parameters were well estimated. For the multidimensional data, the correlations between the estimated item discrimination and the average (as well as the sum of the) dimensional discrimination were greater than the correlations between the estimated item discrimination and the individual dimensional discriminations. Fidelity coefficients between the mean trait level and the trait level estimate (θ) were greater than those between θ and the latent traits. The impact of equating on accuracy indexes in a multidimensional context is discussed. Index terms: dimensionality, graded response model, IRT, marginal maximum likelihood estimation, polytomous models.