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Further topics

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Further topics

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Further topics book

Further topics

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Further topics book

ByP. McCullagh, J.A. Nelder
BookGeneralized Linear Models

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Edition 2nd Edition
First Published 1983
Imprint Routledge
Pages 14
eBook ISBN 9780203753736

ABSTRACT

This chapter describes a number of topics related to generalize linear models, some of which are of current research interest. In the case of full exponential-family models with canonical link function, such as linear logistic models for binomial data, log-linear models for Poisson data, inverse linear models for exponential data, the approximate bias of the maximum-likelihood estimate can be obtained by a very simple supplementary computation are described. The largest biases here are about 10% of a standard error. In cases of marginal statistical significance biases of this magnitude could have a small effect on the conclusions, but they are unlikely to be of any consequence in example. For non-canonical models the tensor expression for the first-order asymptotic bias of ß^ is a little more complicated because it involves the covariance between the vector of first-order derivatives and the matrix of second-order derivatives of the log-likelihood function.

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