Response surface model diagnosis in two-way tables

Graphical model diagnosis procedures for two-way tables have already been proposed by Mandel, as well as by Bradu and Gabriel who used Gabriel's biplot as a main tool. In this paper, a graphical model diagnosis extending Mandel's approach is developed. Response surface models are obtained whereby the response is expressed in terms of ‘truth-connected’ latent variates and, ultimately, in terms of originally measured external variates. Meaningful models are obtained in some cases, accurate smoothing and interpolation algorithms in others. As a by–product, Euclidean maps, which represent a twodimensional scaling (for rows or columns) also displaying ,ANOVA features, are obtained. To an extent, these maps can be viewed as a substitute for a model in the event of partial failure of the modelling operation.