Generalized Self-Consistency: Multinomial logit model and Poisson likelihood.

Journal of Statistical Planning and Inference
Alex Tsodikov, Solomon Chefo

Abstract

A generalized self-consistency approach to maximum likelihood estimation (MLE) and model building was developed in (Tsodikov, 2003) and applied to a survival analysis problem. We extend the framework to obtain second-order results such as information matrix and properties of the variance. Multinomial model motivates the paper and is used throughout as an example. Computational challenges with the multinomial likelihood motivated Baker (1994) to develop the Multinomial-Poisson (MP) transformation for a large variety of regression models with multinomial likelihood kernel. Multinomial regression is transformed into a Poisson regression at the cost of augmenting model parameters and restricting the problem to discrete covariates. Imposing normalization restrictions by means of Lagrange multipliers (Lang, 1996) justifies the approach. Using the self-consistency framework we develop an alternative solution to multinomial model fitting that does not require augmenting parameters while allowing for a Poisson likelihood and arbitrary covariate structures. Normalization restrictions are imposed by averaging over artificial "missing data" (fake mixture). Lack of probabilistic interpretation at the "complete-data" level makes the use of t...Continue Reading

References

Aug 1, 2003·Journal of the Royal Statistical Society. Series B, Statistical Methodology·A Tsodikov

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Citations

Apr 13, 2010·Journal of Statistical Planning and Inference·Shufang Wang, Alex Tsodikov
May 20, 2009·Statistics in Medicine·Solomon Chefo, Alex Tsodikov
Mar 11, 2017·Journal of Biopharmaceutical Statistics·Olga MarchenkoYngvil Kloster Thomas

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