Orlando and Thissen (2000) developed an item fit statistic for binary item response theory (IRT) models known as S-X[superscript 2]. This article generalizes their statistic to polytomous unfolding models. Four alternative formulations of S-X[superscript 2] are developed for the generalized graded unfolding model (GGUM). The GGUM is a…

The performance of five simple multiple imputation methods for dealing with missing data were compared. In addition, random imputation and multivariate normal imputation were used as lower and upper benchmark, respectively. Test data were simulated and item scores were deleted such that they were either missing completely at random, missing at…

The effectiveness of 19 methods of smoothing was investigated as those methods apply to the equipercentile method of test equating. Seven methods involved smoothing the score distribution before the tests were equated (presmoothing). Seven involved smoothing the resultant points after the equating (postsmoothing). Five methods involved combining…

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…