[R] Interpreting Poisson GLM coefficients into everyday language

[David Winsemius]

On Jan 15, 2010, at 4:50 PM, Shawn Morrison wrote:

> Is there a readily available function to calculate the effect of  
> variables from a poisson GLM on the response variable?
>
> My situation is as follows:
>
> I have developed a poisson GLM model and have obtained the  
> coefficients, SEs, etc However, I am somewhat stuck on interpreting  
> a coefficient in everyday language.
> For example:
>
> Y = dependent variable (count data)
> A = independent variable (continuous)
> B = independent variable (continuous)
>
>
> The hypothetical regression equation is:
>
>  [I used natural logs for A]

Assuming that -0.19 was an estimated coefficient in a glm  model  
specified with a formula of:
  Y ~  A + log(B+1) , then you most likely got a model fit with a log  
link (the default for Poisson models) in addition to the log transform  
you applied . So you may have unnecessarily used log transforms.

Then the expected value of Y|log(B+1)  for  E(Y|log(B+1)=1), would be  
exp(-0.19) times that of E(Y|log(B+1)=0). You may have confused things  
a bit by using log(B+1).

a) Did you have zero values for B?
b) Was there really a need to transform A and  B in that manner? You  
ended up with a log(log()) transform.

>
> I want to be able to say that changing B by one unit has a  
> corresponding ___% decrease in Y.
>
> How do I calculate the % change in Y caused by changes in B? Is  
> there an R function, or a bit of code that will do the trick? How do  
> these calculations affect the SEs?
>
> Thank you,
>

> and provide commented, minimal, self-contained, reproducible code.
                                ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Code. We want code.
-- 


David Winsemius, MD
Heritage Laboratories
West Hartford, CT