Leverage in Least Squares Additive-Plus-Multiplicative Fits for Two-Way Tables

Abstract

Abstract An additive-plus-multiplicative model can describe both main effects and row x column interactions in two-way tables of data. When each cell contains exactly one observation, a least squares fit for this nonlinear model calculates the main effects, using means of rows and columns, and then fits a multiplicative term to the additive residuals, using the singular value decomposition. A natural extension of the hat matrix for a linear model yields a definition of leverage that provides insights about the impact of erroneous data values on the fit. Theoretical and numerical investigations reveal the complex nature of leverage for this nonlinear model.