What's the difference between B and Exp(B) in GLM? And is it more correct to replace B with β?
I don't need an extremely detailed answer about the theory behind it.
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1$\begingroup$ Could you please explain what you mean by "B" and "$\beta$"? In the context these could be various versions of coefficients, coefficient estimates, standardized coefficients, and standardized estimates, making it unclear what your question actually is. $\endgroup$– whuber ♦Commented May 25, 2022 at 15:50
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Using the log link the coefficients are on the log scale so for ease of interpretation most people exponentiate them.
Greek letters are used for the population vales so the sample value is usually represented as $b$ not $\beta$. In fact since it is an estimate of $\beta$ you can write it as $\hat\beta$
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$\begingroup$ This makes sense only for binary variables coded as 0/1. Otherwise, exponentiating the coefficient seems to have a rather confusing and indirect interpretation, because there is no readily interpretable relationship between $\exp(x\beta)$ (which is involved in the conditional expectation) and $\exp(\beta)$ generally. $\endgroup$– whuber ♦Commented May 25, 2022 at 15:49
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$\begingroup$ @whuber in fact I was thinking more of Poisson regression. $\endgroup$– mdeweyCommented May 25, 2022 at 17:24