zbMATH — the first resource for mathematics

Leverage in least squares additive-plus-multiplicative fits for two-way tables. (English) Zbl 0546.62045
Summary: An additive-plus-multiplicative model can describe both main effects and row \(\times\) 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 row 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.

62J10 Analysis of variance and covariance (ANOVA)
Full Text: DOI