Rasch used a Poisson model to analyze errors and speed in reading tests. An important property of the Poisson distribution is that the mean and variance are equal. However, in social science research, it is very common for the variance to be greater than the mean (i.e., the data are overdispersed). This study embeds the Rasch model within an…

Assessing individual change is an important topic in both psychological and educational measurement. An adaptive measurement of change (AMC) method had previously been shown to exhibit greater efficiency in detecting change than conventional nonadaptive methods. However, little work had been done to compare different procedures within the AMC…

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…

U.S. state educational testing programs administer tests to track student progress and hold schools accountable for educational outcomes. Methods from item response theory, especially Rasch models, are usually used to equate different forms of a test. The most popular method for estimating Rasch models yields inconsistent estimates and relies on…

Through simulation, the power of the U3 statistic was compared with the power of one of the simplest person-fit statistics, the sum of the number of Guttman errors. In most cases, a weighted version of the latter statistic performed as well as the U3 statistic. (SLD)

Using simulation, the effect that misspecification of elements in the weight matrix has on estimates of basic parameters of the linear logistic test model was studied. Results indicate that, because specifying elements of the weight matrix is a subjective process, it must be done with great care. (SLD)

Eight independent variables (differential item functioning [DIF] detection method, purification procedure, item response model, mean latent trait difference between groups, test length, DIF pattern, magnitude of DIF, and percentage of DIF items) were manipulated, and two dependent variables (Type I error and power) were assessed through…