# Interpreting a Negative Binomial Regression

I've produced a negative binomial regression where the dependent variable is the number of AIDS-related laws passed by each of the US's fifty states in 1989, with the independent variable of legislative session length (unit of analysis = 1 day) and various other control variables. The coefficient for the legislative session length variable is .0013589 (p , 0.5).

Based on the above, can I make the following calculation about the percentage likelihood that a state would pass an additional AIDS law:

(e^(.0013589*100))-1 = 1.145

Hence:

Controlling for all these other factors, I estimate that an extra 100 legislative days increased the likelihood that a state would enact an additional AIDS bill by an average of 15 per cent.

Thanks in advance for your help! If the above is not correct, then I'd really appreciate any tips about expressing the coefficient's effect in substantive terms.

• Should not (e^(.0013589*100))-1 be equal to 0.145? Commented Aug 24, 2022 at 0:21
• Sorry, yes. Hence the figure of 15% Commented Aug 24, 2022 at 0:28

The coefficient estimates are their effects on $$log(\mu)$$ scale by default, so the interpretation of the coefficient is that for every one unit increase in legislative days, you see 0.0013589 times more AIDs laws passed.
The negative binomial regression does not yield a likelihood, or a percentage or anything like that, so the interpretation of the impact of legislative days on AIDs laws passing is incorrect. $$e^{0.0013589*100}=1.145$$ is saying that on the response (count) scale, you'd see 1.145 more laws if the length of the session was 100 days, if all other variables were equal. Not sure why you subtracted the 1.