|From||"Cavallo, Alexander" <email@example.com>|
|To||"'Statalist (firstname.lastname@example.org)'" <email@example.com>|
|Subject||st: GLM question|
|Date||Wed, 9 Jun 2004 14:17:51 -0500|
I am confused about the GLM model using normal errors and log link. In Hardin and Hilbe's book, "Generalized Linear Models and Extensions" there is the following quote on page 59:
"A better approach is to internalize withing the model itself the log transformation of the response. The log link in effect logs the linear predictor, or x*beta, rather than the response to linearize the relationship between the response and predictors. .... The implementation of a log link within the ML algorithm is straightfoward - simple substitute ln(x*beta) for each instance of x*beta in the log-likelihood function. ... Creating a log-normal, or log-linked Gaussian, model using the standard IRLS algorithm is only a bit more complicated ... we must change the link function from eta=mu to eta=ln(mu), and the inverse link function from mu=eta to mu=exp(eta)."
For both ML and IRLS I thought we need to replace each instance of mu or x*beta in the log-likelihood function with exp(x*beta), I don't understand why to use the link function log for ML but the inverse link function exp for IRLS.
Can anyone explain?
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