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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.

##### MSC:
 62J10 Analysis of variance and covariance (ANOVA)
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