Interpreting IRR negative binomial and percentage

[Steve Mullingan]

Hi all,

My dependent variable is a count variable ranging from 10 to 1900. The independent variable ranges from 0 to 100.
Applying negative binomial regression, a IRR of 1.000854 is obtained for indepvar. This can be interpreted as: for every unit increase in indepvar, the rate for depvar is expected to increase with a factor of 1.000854 when holding other variables constant.

I am wondering if I can give a bit more meaning to this statistic by converting it to a percentage. Does anyone have any ideas as I am not sure how to do this with IRRs.

[Maarten Buis]

If you multiply a number by a factor f, then it changes by (f-1)*100%, e.g. if you multiply a number by 1.5, than it increases 50% or if you multiply a number by 0.5, then it decreases 50% (changes by -50%).

So in your case a unit increase in x leads to an increase in the rate of 0.09%.

You could also change the unit of your independent variable by dividing it by 10. That is the same as saying 10 points increase in x leads to an increase in the rate of almost 1 percent.

[Faradj Koliev]

Thanks Maarten Buis. This was what I was looking for. It seems pretty straightforward for continuous variables, but how convert irr values to a percentage points for binary variables?

Lets say that this binary variable is Democracy (=1) and gives me the irr value of 1.14. Then: (1-1.14)*100=14%. How do I interpret that? Can I say that Democracy increases Y with 14% theán nondemocracy?

If you multiply a number by a factor f, then it changes by (f-1)*100%, e.g. if you multiply a number by 1.5, than it increases 50% or if you multiply a number by 0.5, then it decreases 50% (changes by -50%).

So in your case a unit increase in x leads to an increase in the rate of 0.09%.

You could also change the unit of your independent variable by dividing it by 10. That is the same as saying 10 points increase in x leads to an increase in the rate of almost 1 percent.

[Faradj Koliev]

To follow-up: I think it would be more proper to say that IRR of 1.14 means that democracies have 14 percent more Y incidents than nondemocracies, right?