Tree Versus Geometric Representation of Tests and Items

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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 at tempted to broaden the scope of models traditionally used, and to apply an additive tree model (ADDTREE) that belongs to the family of network models. Correla tion matrices were obtained from three studies and were analyzed using two representation models: Smallest Space Analysis (ssA), which is a multidimen sional scaling model, and ADDTREE. The results of both analyses were compared for the two criteria of goodness of fit and interpretability. To enable a com parison with the more traditional factor-analytic ap proach, the data were also subjected to principal com ponents 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 di mensions. ADDTREE'S close fit to the data and its co herence of presentation make it a convenient means of representing tests and items. Index terms: additive trees, ADDTREE, factor analysis, hierarchical cluster ing, multidimensional scaling, Smallest Space Analy sis.