Some Empirical Results Related to the Robustness of the Rasch Model

Abstract

The primary purpose of this study was to investigate the invariance properties of the Rasch model using data from standardized achievement tests that were not constructed to conform to the Rasch model. The item responses of approximately '3,400 examinees (Grades 9, 10, 11, and 12) to four separately timed sections of the Iowa Tests of Educational Development were analyzed. The results indicated that the Rasch model does yield reasonably invariant item parameter and ability parameter estimates for different tests and different examinee groups, even though the assumptions of the model are not met.As noted by many measurement experts, the use of latent trait models may help solve some of the measurement problems frequently encountered by practitioners (e.g., linking and equating of tests and building item banks). However, these models usually require rather strong assumptions about the nature of the data. The major assumption of all latent trait models is unidimensionality or, equivalently, local independence of items. Additional assumptions are required for each specific latent trait model. For dichotomously scored items, the oneparameter logistic, or Rasch, model, is the simplest latent trait model and consequently makes the most restrictive assumptions.

Unidimensionality and Vertical Equating With the Rasch Model

“…Since the two ability estimates would have the same expected value if the tests were accurately equated, a comparison of the difference between them was used to evaluate the equating results obtained. Using a procedure employed by Wright (1968), Whitely and Dawis (1974), Linn (1978, 1979a) and Forsyth, Saisangjan and Gilmer (1981), a standardized difference score (Dr) was obtained for each student as follows: To examine the distribution of these differences, average values were also plotted at selected points along the ability scale for both samples.…”

An Application of the Three-Parameter IRT Model to Vertical Equating

“…One of these, unidimensionality, requires that there be only one trait underlying the examinees' responses to the test items. Although this assumption is never strictly met in practice, there is evidence that IRT equating methods are somewhat robust to violations of it (Cook & Eignor, 1982;Forsyth, Saisangjan, & Gilmer, 1981;Petersen, Cook, & Stocking, 1983). Other assumptions, such as a specified functional form for the item characteristic curves, are also required, though in a practical sense, the issue is not so much how well the data fit the model as how well the model will perform with real data in a real testing situation.…”

Estimation des paramètres d’item et de sujet à partir du modèle de Rasch

“…de plus, dans le cas de la modélisation à trois paramètres, l'estimation du paramètre de pseudo-chance nécessite un grand nombre de sujets qui affichent un niveau d'habileté faible : une situation qui est difficile à respecter si l'échan-tillon de sujets est trop petit. dans ce contexte, plusieurs auteurs ont démon-tré que le modèle de Rasch respecte de façon raisonnable le principe d'invariance des items et des sujets pour différents tests et différents groupes de répondants (Forsyth, sarsangjan, & Gilmer, 1981) …”