This paper addresses the problem of inference for a
multinomial regression model in the presence of likelihood monotonicity. This
paper proposes translating the multinomial regression problem into a
conditional logistic regression problem, using existing techniques to reduce
this conditional logistic regression problem to one with fewer observations and
fewer covariates, such that probabilities for the canonical sufficient
statistic of interest, conditional on remaining sufficient statistics, are
identical, and translating this conditional logistic regression problem back to
the multinomial regression setting. This reduced multinomial regression problem
does not exhibit monotonicity of its likelihood, and so conventional asymptotic
techniques can be used.
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