In selected-response assessments such as attitude surveys with Likert-type rating scales, examinees often select from rating scale categories to reflect their locations on a construct. Researchers have observed that some examinees exhibit "response styles," which are systematic patterns of responses in which examinees are more likely to…

About 45 R packages to analyze data using item response theory (IRT) have been developed over the last decade. This article introduces these 45 R packages with their descriptions and features. It also describes possible advanced IRT models using R packages, as well as dichotomous and polytomous IRT models, and R packages that contain applications…

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 purpose of this research is to demonstrate that a systematic approach to the graphical analysis of Rasch model residuals can lead to an increased understanding of ordered response data, and that residual patterns do change in predictable ways, and that summary statistics need not be the only piece of evidence for assuring the fit between model…

This paper illustrates the transformation of a raw data matrix into a matrix of associations, and then into a factor matrix. Factor analysis attempts to distill the most important relationships among a set of variables, thereby permitting some theoretical simplification. In this heuristic data, a correlation matrix was derived to display…