Conceptualized eight different types of measurement models for a test composed of testlets and studied the goodness of fit of those models to data using data from the Iowa Tests of Basic Skills and simulated data. The essentially tau-equivalent model and the congeneric model provided worse model fit than the other measurement models. (SLD)

A Rasch-type analysis is presented for multiple-choice items in which one parameter is assigned to each distractor. Results of a small simulation study show that the parameter recovery of the distractor model is very satisfactory. Analysis of a real dataset shows that some items fit the Rasch model rather than the distractor model. (SLD)

A new item-fit index is proposed that is both a descriptive measure of deviance of single items and an index for statistical inference. This index is based on assumptions of the dichotomous and polytomous Rasch models for items with ordered categories. A simulation study is described. (SLD)

A method is proposed to assess the importance of differential item functioning (DIF) by estimating the largest possible fraction of the population in which DIF does not occur, or equivalently, the smallest possible portion of the population in which DIF may occur. The approach is based on latent class (C. C. Clogg, 1981) or mixture concepts, and…

A confirmatory approach to assessing test structure using multidimensional item response theory (MIRT) was developed and evaluated. The approach involved adding to the exponent of the MIRT model an item structure matrix that allows the user to specify the ability dimensions measured by an item. Various combinations of item structures were fit to…

This paper will discuss the results of a series of computer simulations comparing the Rasch logistic model to a series of models departing to various degrees from its assumption of equal discrimination power for all items. The results have implications for test construction and test scoring, indicating how closely the conventional raw score…

Since all commonly used latent trait models assume a unidimensional test, the applicability of the procedure to obviously multidimensional tests is questionable. This paper presents the results of the application of latent trait, traditional, and factor analyses to a series of actual and hypothetical tests that vary in factoral complexity.…

The quality of fit between the data and the measurement model is fundamental to any discussion of results. Fit has been the subject of inquiry since as early as the 1920s. Most early explorations concentrated on assessing global fit or subset fits on fixed length, traditional paper and pencil tests given as a single unit. The detection of aberrant…

The purpose of the present research was to study, systematically, the "goodness-of-fit" of the one-, two-, and three-parameter logistic models. We studied, using computer-simulated test data, the effects of four variables: variation in item discrimination parameters, the average value of the pseudo-chance level parameters, test length,…

This paper describes an item response theory (IRT) based method of differential item functioning (DIF) detection that involves neither separate calibration nor ability grouping. IRT is used to generate residual scores, scores free of the effects of person or group ability and item difficulty. Analysis of variance is then used to test the group…

The efficacy of employing subsets of items from a calibrated item pool to estimate the Rasch model person parameters was investigated. Specifically, the degree of invariance of Rasch model ability-parameter estimates was examined across differing collections of simulated items. The ability-parameter estimates were obtained from a simulation of…