Theory of linear and integer programming
Theory of linear and integer programming
Fundamentals of statistical exponential families: with applications in statistical decision theory
Fundamentals of statistical exponential families: with applications in statistical decision theory
Indicator models in social mobility tables
Computational Statistics & Data Analysis
Algebraic Statistics for Computational Biology
Algebraic Statistics for Computational Biology
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The paper considers general multiplicative models for complete and incomplete contingency tables that generalize log-linear and several other models and are entirely coordinate free. Sufficient conditions for the existence of maximum likelihood estimates under these models are given, and it is shown that the usual equivalence between multinomial and Poisson likelihoods holds if and only if an overall effect is present in the model. If such an effect is not assumed, the model becomes a curved exponential family and a related mixed parameterization is given that relies on non-homogeneous odds ratios. Several examples are presented to illustrate the properties and use of such models.