The Biplot as a Diagnostic Tool for Models of Two-Way Tables

The biplot graphical display of matrices is proposed as a data analytic tool for diagnosing the type of model to fit the data. Rows and columns of the data matrix are represented by markers—the diagnosis proceeds by examining these markers for collinearity. Thus, for example. if set I of row markers are collinear and a set J of column markers are also collinear. a Tukey degree-of-freedom-for-non-additivity is diagnosed for the submatrix of these I-rows and J-columns: if the two lines are at 90°. an additive model is diagnosed. Mandel type models are similarly diagnosed when either the row or the column markers are collinear but not both. Illustrations from physical science data show how simple biplot diagnostic modeling is and how many features of the data are revealed. Of particular interest are biplots of three-way layouts which allow visual inspection of main effects and interactions.