Poisson Regression Interpretation

#1
Hello everybody,

I have a data where I am testing the effect of some independent variables on the count of a dependent variable. So I did a Poisson regression and got the following results. poisson regression data.jpg

In the above table, all my correlations seem significant, except from var1. My issue is how to interpret these results. I am trying to compare the effects of my independent variables and I am not sure how the results can help me with that. For example, can I say that var3 is more correlated than var2 since its negative coefficient is smaller. Similarly, can I say that var4 is more correlated with the dependent variable than var5. Besides, what would be a good coefficient? Are there any commonly used ranges for strong, weak and mild correlations (like the ones for Pearson Correlation or Cohen D)? Do I need to calculate an effect size to rank my variables instead of using the coefficient? If yes, which one is the more suited with Poisson Regression (I am not sure if Cohen D would be a good fit here).

Thanks for your help.
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
Just report the estimates along with the confidence intervals. Also, do you need to exponeniate the coefficients in order to get the relative mean values?

It is up to your audience to interpret if the estimates are strong, weak, etc., since that in contextual. But the Z-values can help you rank order them in your mind.
 

katxt

Active Member
#4
Just to give you an idea of the sort of values you are likely to get when you finish you interpretation, you could try the usual OLS regression where the coefficients often have real world meanings which should be close to your final Poisson interpretations.
 
#6
I haven't tried OLS, because I thought Poisson Regression is the natural choice here since my dependent variable is a count. But it is easy to try with the tool we have now days. I am writing a paper about the above data and just want to present the results in a rigorous way, to anticipate any critique from the reviewers. I want to draw the right conclusion out of the results and avoid make the results say more than they should (e.g. the results show there is a strong negative correlation between var3 and the dependent variable). This is the reason why I asked your help guys.
 

Dason

Ambassador to the humans
#7
My main concern with Poisson regression especially when presenting any sort of p-values is that there might be overdispersion. I like that you're thinking about Poisson for counts but you sound like somebody that wants to cover their bases so maybe checking for overdispersion would help alleviate any of those concerns.
 

katxt

Active Member
#8
@katxt - is there enough information presented to have suspicion that OLS may be a good fit for these data?
I'm not suggesting that OLS is a better model, just that the results from OLS are easily interpreted and should give an indication of what you can expect from the Poisson after they have been manipulated to give real world meanings.