Fuzzy sets have experienced multiple expansions since their conception to enhance their capacity to convey complex information. Intuitionistic fuzzy sets, image fuzzy sets, q-rung orthopair fuzzy sets, and neutrosophic sets are a few of these extensions. Researchers and academics have acquired a lot of information about their theories and methods…

Although definitions of validity have evolved considerably since L. J. Cronbach and P. E. Meehl's classic (1955) review, contemporary validity research continues to emphasize correlational analyses assessing predictor-criterion relationships, with most outcome criteria being self-reports. The present article describes an alternative way of…

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…

This comprehensive "Handbook" focuses on the most used polytomous item response theory (IRT) models. These models help us understand the interaction between examinees and test questions where the questions have various response categories. The book reviews all of the major models and includes discussions about how and where the models…

Recent work has shown that multidimensionally scoring responses from different tests can provide better ability estimates. For educational assessment data, applications of this approach have been limited to binary scores. Of the different variants, the de la Torre and Patz model is considered more general because implementing the scoring procedure…

The purpose of this book is to make it possible for measurement specialists to solve practical testing problems through the use of item response theory (IRT). The topics, organization, and presentation are those used in a 4-week seminar held each summer for the past several years. The material is organized to facilitate understanding; all related…

This paper presents an introduction to the use of latent trait models for the estimation of domain scores. It was shown that these models provided an advantage over classical test theory and binomial error models in that unbiased estimates of true domain scores could be obtained even when items were not randomly selected from a universe of items.…

Some examinees' test-taking behavior may be so idiosyncratic that their scores are not comparable to the scores of more typical examinees. Appropriateness indices, which provide quantitative measures of response-pattern atypicality, can be viewed as statistics for testing a null hypothesis of normal test-taking behavior against an alternative…

A common problem in practical educational research is that of perfect scores which result when latent trait models are used. A simple procedure for managing the perfect and zero response problem encountered in converting test scores into measures is presented. It allows the test user to chose among two or three reasonable finite representations of…

Presents a unified concept of test validity that integrates both the scientific and ethical considerations of test interpretation and use. Argues that the appropriateness, meaningfulness, and usefulness of score-based inferences are inseparable, and that this integration is based on construct validity. (FMW)

Techniques derived from item response theory are useful for estimating the reliability of test classification above and below the cutting score. Test developers can construct a test whose information is peaked in the region of the cutting score; users can select a test which provides the most information in this region. The Cut-Score…

Two methods of 'equating' tests using item response theory (IRT) are compared, one using true scores, the other using the estimated distribution of observed scores. On the data studied, they yield almost indistinguishable results. This is a reassuring result for users of IRT equating methods. (Author)

The Portland (Oregon) Public Schools undertook studies of regression based on a three-year data base of fall and spring test results in grades 3 through 8 in reading, language usage and mathematics. The objective of these regression studies was to determine the amount of correction for regression to the mean needed to accurately represent the…

In latent trait theory the latent space, or space of the hypothetical construct, is usually represented by some unidimensional or multi-dimensional continuum of real numbers. Like the latent space, the item response can either be treated as a discrete variable or as a continuous variable. Latent trait theory relates the item response to the latent…