Profile data abound in a broad range of research settings. Often it is of considerable theoretical importance to address specific structural questions with regard to the major pattern as included in such data. A key challenge in this regard pertains to identifying which type of interaction (double ordinal, mixed ordinal/disordinal, double…

This paper introduces five commonly used approaches to analyzing multiple-choice test data. They are classical test theory, factor analysis, cluster analysis, item response theory, and model analysis. Brief descriptions of the goals and algorithms of these approaches are provided, together with examples illustrating their applications in physics…