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We propose a method for estimating the parameters of contingency table models, which is motivated by a geometrical idea. Our method--bisector regression for contingency tables (BRCT)--is based on a nested structure of contingency table models. Our method estimates parameters corresponding to the interactions of lower orders after estimating or eliminating those of higher orders. BRCTgenerates a sequence of parameter estimates, each element of which represents a model and a parameter estimate. The length of the sequence is equal to the number of parameters, which is much smaller than the total number of models. We describe the BRCTalgorithm and show an example. We provide explanations for two cases: (a) two factors and (b) K factors. [ABSTRACT FROM AUTHOR]