Selection effects and unidimensionality in item response theory
David A. Grayson · British Journal of Mathematical and Statistical Psychology · 1990
In the factor‐analytic perspective on unidimensional item response theory (IRT), the latent trait is construed as a single common factor to the items, each item having an independent residual which determines the item characteristic curve (ICC). It is possible that such residual terms have a component which is ‘stable’ and reflects some attribute of the subjects being measured other than the trait in common to all the items (the common factor). That is, heuristically, the ‘residual’ may consist of ‘specific’ and ‘error’ components. As such, comparison of subpopulations on such a test may confound selection effects on the common factor with selection effects on such stable components of the residuals, vitiating inference from manifest test response differences to common factor differences. A technique for exploratory use in assessing the presence of such (undesirable) stable residuals using repeated measures data is discussed, together with applications. The technique is of broader potential application, allowing one to use repeated measures data to search for ‘user‐defined’ violations of unidimensionality. It assumes the existence of a sufficient score for the common factor, and is thus an exact technique when a Rasch model is assumed.