Mixed Rasch Models for Measurement in Cognitive Psychology

Abstract

To apply standard unidimensional IRT models to ability measurement, it must be assumed that individuals at the same level of performance are in fact comparable. That is, individuals with the same estimate on the latent trait are interchangeable and thus can have identical interpretations given to their scores. Such interpretations, of course, depend on the construct validity of the trait measure, which includes both the construct representation and nomothetic span aspects (Embretson, 1983). The construct representation aspect of validity involves the meaning of the construct, in terms of the processes, strategies, and knowledge that are directly involved in performance. Construct representation is an aspect of internal validity. The nomothetic span aspect concerns the significance of the trait, which includes the relationship of trait scores to other measures, demographics and criteria. Nomothetic span is primarily the external validity of the measure.