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A poisson regression is a GLM with a log link function. So if I have count data, then preprocess it by taking the log before running a least-squares regression, is that equivalent to, or related to, running a poisson regression? |
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Almost, as the loss function is wrong. In Poisson regression you don't want to minimize a log-square loss (i.e., (log Y - f(x))^2) but the negative likelihood loss over the poisson regression model, or -(y f(x) -exp(f(x))). See the Poisson regression article on wikipedia for more details. intuitively it has to do with the fact that the noise is heteroskedastic. ordinary least squares assumes the noise (squared error) to be independent of x (which implies independence with y). with poisson regression, the variance in the noise is correlated with y. to this kind of regression properly, you need to do weighted least squares.
(Mar 20 '11 at 20:07)
Travis Wolfe
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