Projective Item Response Model for Test-Independent Measurement

Abstract

The problem of fitting unidimensional item-response models to potentially multidimensional data has been extensively studied. The focus of this article is on response data that contains a major dimension of interest but that may also contain minor nuisance dimensions. Because fitting a unidimensional model to multidimensional data results in ability estimates that represent a combination of the major and minor dimensions, such a procedure tends to produce ability estimates that cannot be compared across different tests targeting the same construct, or even across different test forms from the same test bank. In this paper, we build upon previous theoretical results in multidimensional IRT and propose a projective IRT framework that allows the projection of multiple dimensions onto a targeted single dimension that is of substantive interest. Two robust versions of standard error estimate for ability score are also evaluated. An important appeal of the projective IRT procedure is that it allows the direct measurement of a targeted construct and valid inference for test-independent ability scores. Through simulation studies, we show that the proposed projective IRT procedure effectively recovers ability scores in the targeted dimension. The procedure involves only a small amount of additional computation over conventional IRT and could have potential applications in areas such as computerized adaptive testing.