A Rasch model for ordered response categories is derived and it is shown that it retains the key features of both the Thurstone and Likert approaches to studying attitude. Key features of the latter approaches are reviewed. Characteristics in common with the Thurstone approach are: statements are scaled with respect to their affective values;…

A method based on the likelihood ratio procedure is presented for use in selecting a measurement model from among the Rasch, two-parameter, and three-parameter logistic latent trait models. (Author/BW)

Six statistical methods for identifying possible sources of bias in standardized test items are presented. The relationship between chi-squared methods and item-response theory methods are also discussed. (Author/BW)

A formula is derived for the asymptotic standard error of a true-score equating by item response theory (IRT). The equating method is applicable when the two tests to be equated are administered to different groups along with an "anchor test." Numerical standard errors are shown for an actual equating 1) comparing the standard errors of…

This paper attempts to provide some initial information about the use of a variety of item response theory (IRT) models in the item selection process; its purpose is to compare the information curves derived from the selection of items characterized by several different IRT models and their associated parameter estimation programs. These…

An upper-asymptote parameter was added to the three-parameter logistic item response model. This four-parameter model was compared to the three-parameter model on four data sets. The fourth parameter increased the likelihood in only two of the four sets. Ability estimates for the students were generally unchanged by the introduction of the fourth…

Two procedures for Rasch, sample-free item calibration are reviewed and compared for accuracy. The theoretically ideal "conditional" procedure is impractical for more than fifteen items. The more practical but biased "unconditional" procedure is discussed in detail. (Author/JKS)

During the past several decades, a new class of measurement theory, called latent trait (or item response) theory, has become popular. Supporters contend that results obtained through the use of this theory prove vastly superior to classical measurement statistics. This paper investigates the use of the Rasch model, one of the more popular latent…

The Pearson and likelihood ratio statistics are frequently used for assessing the absolute fit of probability models. Researchers are often interested in comparing fits provided by different models which may have a subsuming or non-subsuming relation. A subsuming relation exists when the parameters of the reduced model form a subset of those…

There are currently three main approaches to parameter estimation in item response theory (IRT): (1) joint maximum likelihood, exemplified by LOGIST, yielding maximum likelihood estimates; (2) marginal maximum likelihood, exemplified by BILOG, yielding maximum likelihood estimates of item parameters (ability parameters can be estimated…

The purposes of this study are: (1) to compare the results of linear, equipercentile, frequency estimation equipercentile and item response theory (IRT) true formula score equating; and (2) to investigate the feasibility of using IRT methods to equate new forms of the Preliminary Scholastic Aptitude Test/National Merit Scholarship Qualifying Test…

This paper develops and applies three nonparametric comparisons of the shapes of two item characteristic surfaces: (1) proportional latent odds; (2) uniform relative difficulty; and (3) item sensitivity. A method is presented for comparing the relative shapes of two item characteristic curves in two examinee populations who were administered an…

The use of item response theory models for analyzing the results of judgmental standard setting studies (the Angoff technique) for establishing minimum pass levels is discussed. A comparison of three methods indicates the traditional approach may not be best. A procedure based on generalizability theory is suggested. (GDC)

Three equating methods were compared in terms of magnitude of scale drift: equipercentile equating, linear equating, and item response theory (IRT) equating. A sample of approximately 2670 cases was selected for each pairing of a form of the Scholastic Aptitude Tests (SAT) and an anchor test. Of the two conventional equating methods,…

A short review of the different estimation procedures that have been used in association with the Rasch model is provided. These procedures include joint, conditional, and marginal maximum likelihood methods; Bayesian methods; minimum chi-square methods; and paired comparison estimation. A comparison of the marginal maximum likelihood estimation…