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Abstract Details
Activity Number:
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574
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Type:
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Contributed
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Date/Time:
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Wednesday, August 3, 2011 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Statistical Computing
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Abstract - #302934 |
Title:
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Iteratively Reweighted Poisson Regression for Fitting Generalized Linear Model with Multiple Responses
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Author(s):
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Yiwen Zhang*+ and Hua Zhou
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Companies:
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North Carolina State University and North Carolina State University
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Address:
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2311 Stinson Drive, Raleigh, NC, 27695,
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Keywords:
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Dirichlet-multinomial ;
GLM ;
MM algorithm ;
multinomial-logit ;
multiple responses ;
negative-multinomial
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Abstract:
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Generalized linear models with multiple responses (MGLMs) are seeing wider use in modern applications such as pattern recognition, document clustering, and image reconstruction. Examples of MGLMs include multinomial-logit models, Dirichlet-multinomial overdispersion models, and negative-multinomial models. Maximum likelihood estimation of MGLMs is difficult due to the high-dimensionality of the parameter space and possible non-concavity of the log-likelihood function. In this article, we propose iteratively reweighted Poisson regression as a unified framework for maximum likelihood estimation of MGLMs. The derivation hinges on the minorization-maximization (MM) principle which generalizes the celebrated expectation-maximization (EM) algorithm. MM algorithm operates by constructing a surrogate function with parameters separated. Optimizing such a surrogate function drives the objective function in the correct direction. This leads to a stable algorithm which possesses good global convergence property and is extremely simple to code. The proposed algorithm is tested on classical and modern examples.
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