Tree versus geometric representation of tests and items

Abstract

Factor-analytic techniques and multidimensional scaling models are the traditional ways of representing the interrelations among tests and items. Both can be classified as geometric approaches. This study attempted to broaden the scope of models traditionally used, and to apply an additive tree model (ADDTREE) that belongs to the family of network models. Correlation matrices were obtained from three studies and were analyzed using two representation models: Smallest Space Analysis (SSA), which is a multidimensional scaling model, and ADDTREE. The results of both analyses were compared for the two criteria of goodness of fit and interpretability. To enable a comparison with the more traditional factor-analytic approach, the data were also subjected to principal components analyses. ADDTREE fared better in both comparisons. Moreover, ADDTREE lends itself readily to an interpretation in terms of hierarchical cluster structure, whereas it is difficult to interpret SSA’s dimensions. ADDTREE’S close fit to the data and its coherence of presentation make it a convenient means of representing tests and items. Index terms: additive trees, ADDTREE, factor analysis, hierarchical clustering, multidimensional scaling, Smallest Space Analysis.