item bias, test bias, DIF, differential test functioning, DTF, SIB, SIBTEST, standardization, simultaneous items bias, valid subtest, bias/DIF, Mantel-Haenszel,

unidimensionality, local independence, test of unidimensionality, latent trait theory, latent structure analysis, item response theory, large sample theory, asymptotic distribution theory, nonparametric test,

No abstract

item response theory, dimensionality, multidimensionality, generalized compensatory model, simple structure, approximate simple structure, genetic algorithm, dimensionally homogeneous item cluster, latent space, test space,

Two simulation studies investigated Type I error performance of two statistical procedures for detecting differential item functioning (DIF): SIBTEST and Mantel‐Haenszel (MH). Because MH and SIBTEST are based on asymptotic distributions requiring “large” numbers of examinees, the first study examined Type 1 error for small sample sizes. No significant Type I error inflation occurred for either procedure. Because MH has the potential for Type I error inflation for non‐Rasch models, the second study used a markedly non‐Rasch test and systematically varied the shape and location of the studied item. When differences in distribution across examinee group of the measured ability were present, both procedures displayed inflated Type 1 error for certain items; MH displayed the greater inflation. Also, both procedures displayed statistically biased estimation of the zero DIF for certain items, though SIBTEST displayed much less than MH. When no latent distributional differences were present, both procedures performed satisfactorily under all conditions.

A multidimensionality-based differential item functioning (DIF)

item response theory, dimensionality, multidimensionality, generalized compensatory model, conditional covariance, information, multidimensional critical ratio function, test space, DETECT, DIMTEST,

According to the weak local independence approach to defining dimensionality, the fundamental quantities for determining a test's dimensional structure are the covariances of item-pair responses conditioned on examinee trait level. This paper describes three dimensionality assessment procedures-HCA/CCPROX, DIMTEST, and DETECT—that use estimates of these conditional covariances. All three procedures are nonparametric ; that is, they do not depend on the functional form of the item response functions. These procedures are applied to a dimensionality study of the LSAT, which illustrates the capacity of the approaches to assess the lack of unidimensionality, identify groups of items manifesting approximate simple structure, determine the number of dominant dimensions, and measure the amount of multidimensionality. Index terms: approximate simple structure, conditional covariance, DETECT , dimensionality, DIMTEST, HCA/CCPROX, hierarchical cluster analysis, IRT, LSAT, local independence, multidimensionality, simple structure.