Historical Perspectives on Invariant Measurement: Guttman, Rasch, and Mokken

The purpose of this study is to describe how Guttman, Rasch, and Mokken approached issues related to invariant measurement. These measurement theorists were chosen to illustrate the evolution of our conceptualizations of invariant measurement during the 20th century within the research tradition of item response theory. Item response theory can be viewed as consisting of nonparametric and parametric scaling models. Invariant measurement consists of requirements related to the item-invariant measurement of individuals, and the sample-invariant calibration of items. Guttman was selected to represent a nonparametric approach to invariant measurement based on a deterministic scaling model, whereas Rasch was selected to represent a parametric approach based on a probabilistic model. Mokken presents a nonparametric approach based on a probabilistic model. Mokken combines aspects of Guttman Scaling with Rasch measurement theory, and provides a nonparametric framework for examining Rasch's requirements for invariant measurement. Key words: history of measurement theoryinvariant measurementGuttman ScalingRasch Measurement TheoryMokken Scalingitem-invariant measurementsample-invariant calibration ACKNOWLEDGMENTS An earlier version of this paper was presented as an invited address to the Rasch Special Interest Group of the American Educational Research Association in Chicago (April 2007).