An introduction to multidimensional measurement using Rasch models

The act of constructing a measure requires a number of important assumptions. Principle among these assumptions is that the construct is unidimensional. In practice there are many instances when the assumption of unidimensionality does not hold, and where the application of a multidimensional measurement model is both technically appropriate and substantively advantageous. In this paper we illustrate the usefulness of a multidimensional approach to measurement with the Multidimensional Random Coefficient Multinomial Logit (MRCML) model, an extension of the unidimensional Rasch model. An empirical example is taken from a collection of embedded assessments administered to 541 students enrolled in middle school science classes with a hands-on science curriculum. Student achievement on these assessments are multidimensional in nature, but can also be treated as consecutive unidimensional estimates, or as is most common, as a composite unidimensional estimate. Structural parameters are estimated for each model using ConQuest, and model fit is compared. Student achievement in science is also compared across models. The multidimensional approach has the best fit to the data, and provides more reliable estimates of student achievement than under the consecutive unidimensional approach. Finally, at an interpretational level, the multidimensional approach may well provide richer information to the classroom teacher about the nature of student achievement.