Generalized Multiplicative Models

Algorithmic Approaches for Fitting Bilinear Models

“…Revisiting some of the results in Green (1986) and Francis and Saint-Pierre (1986), it appears that such bilinear (or multiplicative) models can be fitted by alternating generalized regressions (successive relaxations) with adapted error terms (normal, Poisson, binomial ... ), link functions (identity, log, logit ... ) and weights (missing entries or structural values). At each step row and column scores are readily obtained by Gram-Schmidt orthogonalisation (least squares regressions).…”