# negative binomial regression coefficients and exp(b)

#### LidoBeach

##### New Member
Thank you so much anyone...
I have the results of a negative binomial where the DV is the log count of meals obtained.
I have continuous predictors and I have my DV back logged, i.e., exp(b) with CIs for easier interpretation in my paper.
The thing is... I am not easily interpreting my exp(b) < 1 because most examples are for ORs and this is not an ORs per se.
For example,
I have days on campus as an IV and health consciousness as an IV
the days exp(b) is ~ 1.13, so I feel comfortable saying for every 1 unit increase (a day) there is a 13% increase in meals.
The health consciousness exp(b) is .80. So for every one point increase in level of health consciousness, there is a _% decrease in meals.
Is it simply a 20% decrease? 1-.80
or a 25% decrease i.e., 1/.80 or is it 28% the beta / by the exp(b) = (-) .22 / .80 .
It does not make sense to say that a one level increase in health consciousness means that a person is .80 times as likely to obtain the meals as a person without a one unit increase -as my DV is continuous not dichotomous.

Much thanks.. my multiple interpretations come from too many google searches!

#### noetsi

##### No cake for spunky
It is often suggested, and this has always made sense to me, that when you have an Odds Ratio less than one, you reverse the value you are maximising in the Dependent variable (say 1 if it was 0) and then interpret the odds ratio this way. That will of course make it greater than one. You then state the interpretation in terms of maximising the 1 not the 0. It does not make substantive difference which level of the DV you maximize - just be clear what you did and why.

#### LidoBeach

##### New Member
Yes noesti I understand and have been told the same thing, however, my DV is not dichotomous and my IV is not categorical, hence the confusion. My DV is the logged count of meals and the exp(b) is the back log, but its still for every 1 unit of my IV there is an increase or decrease in NUMBER of meals - not 0 or 1 meals. Make sense?

#### CB

##### Super Moderator
I have the results of a negative binomial where the DV is the log count of meals obtained.
Just to clarify: Do you mean that you have used a negative binomial model with a log link (the default, canonical link applied automatically in most software), with the DV simply being the count of meals? Or have you manually log-transformed your DV and then run a negative binomial regression?

#### LidoBeach

##### New Member
Just to clarify: Do you mean that you have used a negative binomial model with a log link (the default, canonical link applied automatically in most software), with the DV simply being the count of meals? Or have you manually log-transformed your DV and then run a negative binomial regression?
You are correct, the program logged the variable and I also used the print solution (exponentiate) option. Here is the table I created from the SPSS output.

B SE exp(b) CI
Health Consciousness -0.22** 0.05 0.80 0.73 0.89

(DV number of meals obtained)