Abstract
Consider a multinomial response model with (k+1) outcomes and p explanatory variables. The general logistic model for the multinomial probabilities results in a matrix of sufficient statistics having kp elements. The means and variances of the sufficient statistics are derived (under the null hypothesis) and can be written as a Kronecker product. Since the sufficient statistics have asymptotic normal distributions, large sample tests can be derived which uses a chi-square statistic. The conditional test for testing if a single explanatory variable affects the response is derived.
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