Statistical process control (SPC) charts have been widely used in the field of educational measurement. The cumulative sum (CUSUM) is an established SPC method to detect aberrant responses for educational assessments. There are many studies that investigated the performance of CUSUM in different test settings. This paper describes the CUSUM…

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…

Although the root-mean squared deviation (RMSD) is a popular statistical measure for evaluating country-specific item-level misfit (i.e., differential item functioning [DIF]) in international large-scale assessment, this paper shows that its sensitivity to detect misfit may depend strongly on the proficiency distribution of the considered…

The recent popularity of models that capture the dynamic coevolution of both network structure and behavior has driven the need for summary indices to assess the adequacy of these models to reproduce dynamic properties of scientific or practical importance. Whereas there are several existing indices for assessing the ability of the model to…

This article provides a brief introduction to the Rasch model. Motivation for using Rasch analyses is provided. Important Rasch model concepts and key aspects of result interpretation are introduced, with major points reinforced using a simulation demonstration. Concrete guidelines are provided regarding sample size and the evaluation of items.

Two Monte Carlo simulation studies investigated the effectiveness of the mean adjusted X[superscript 2]/df statistic proposed by Drasgow and colleagues and, because of problems with the method, a new approach for assessing the goodness of fit of an item response theory model was developed. It has been previously recommended that mean adjusted…

In multilevel structural equation modeling, the "standard" approach to evaluating the goodness of model fit has a potential limitation in detecting the lack of fit at the higher level. Level-specific model fit evaluation can address this limitation and is more informative in locating the source of lack of model fit. We proposed level-specific test…

Two-level data sets are frequently encountered in social and behavioral science research. They arise when observations are drawn from a known hierarchical structure, such as when individuals are randomly drawn from groups that are randomly drawn from a target population. Although 2-level data analysis in the context of structural equation modeling…

Most personality tests are made up of Likert-type items and analyzed by means of factor analysis (FA). In this type of application, the fit of the model at the level of individual respondents is almost never assessed. This article proposes procedures for assessing individual fit (scalability). The procedures are intended for the analysis of…

Higher-order approximations to the distributions of fit indexes for structural equation models under fixed alternative hypotheses are obtained in nonnormal samples as well as normal ones. The fit indexes include the normal-theory likelihood ratio chi-square statistic for a posited model, the corresponding statistic for the baseline model of…

Different sets of uniqueness constraints may lead to different fit results when applied to the same data in confirmatory factor analysis. Provides several examples of this phenomenon in simulated data and describes reasons for the variation in fit results. Discusses the choice of uniqueness constraints under these circumstances. (SLD)

Points out two concerns with recent research by F. Li and others (2000) and T. Duncan and others (1999) that extended the structural equation model of latent interactions developed by K. Joreskog and F. Yang (1996) to latent growth modeling. Used mathematical derivation and a comparison of alternative models fitted to simulated data to develop a…

Exploratory factor analysis (EFA) is a frequently used multivariate analysis technique in statistics. Jennrich and Sampson (1966) solved a significant EFA factor loading matrix rotation problem by deriving the direct Quartimin rotation. Jennrich was also the first to develop standard errors for rotated solutions, although these have still not made…

An item response model is proposed for the analysis of continuous response formats in an item response theory (IRT) framework. With such formats, respondents are asked to report their response as a mark on a fixed-length graphical segment whose ends are labeled with extreme responses. An interpolation process is proposed as the response mechanism…

Complete response vectors of all answer options in multiple-choice items can be used to estimate ability. The rising selection ratios criterion is necessary for scoring individuals because it implies that estimated ability always increases when the correct alternative is selected. This paper introduces the generalized DLT model, which assumes…