Model Diagnosis in Two-Way Tables by Means of Row and Column Euclidean Maps

摘要

Graphical model diagnosis procedures for two-way nxm tables were already proposed by Mandel and by Bradu and Gabriel, the latter using Gabriels biplot as a main tool. Manel's approach is reinterpreted within the framework of Response Surface Models, and considerably extended. Euclidean Maps are introduced; these are graphical displays of rows and columns respectively, based on parameter estimates for the Multiplicative Interaction model. Besides yielding two-dimensional displays for the euclidean spatial structure of the rows and columns as points in R(supra n) and R (supra m) respectively, these plots which are computationally easy to obtain, permit a better model diagnosis which also applies to nonlinear response surfaces expressed in terms of latent variates, which are well described by Taylor expansions going up to second order terms. Extending the approach of Bradu and Gabriel, the biplot of the residuals matrix is used to diagnose Response Surface Models where the Taylor expansion of the response function goes beyond the terms of second order.