Graphical representation of multidimensional item response theory analyses

Abstract

This paper illustrates how graphical analyses can enhance the interpretation and understanding of multidimensional item response theory (IRT) analyses. Many unidimensional IRT concepts, such as item response functions and information functions, can be extended to multiple dimensions; however, as dimensionality increases, new problems and issues arise, most notably how to represent these features within a multidimensional framework. Examples are provided of several different graphical representations, including item response surfaces, information vectors, and centroid plots of conditional two-dimensional trait distributions. All graphs are intended to supplement quantitative and substantive analyses and thereby assist the test practitioner in determining more precisely such information as the construct validity of a test, the degree of measurement precision, and the consistency of interpretation of the number-correct score scale. Index terms: dimensionality, graphical analysis, multidimensional item response theory, test analysis.