Negative Binomial Regression: coefficient interpretation

Question

How should coefficients (intercept, categorical variable, continuous variable) in a negative binomial regression model be interpreted? What is the base formula behind the regression (such as for Poisson regression, it is $\ln(\mu)=\beta_0+\beta_1 x_1 + \dots$)?

Below I have an example output from my specific model that I want to interpret, where seizure.rate is a count variable and treatment categorical (placebo vs. non-placebo).

Call:
glm.nb(formula = seizure.rate2 ~ treatment2, data = epilepsy2, 
    init.theta = 1.499060952, link = log)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.3504  -0.8814  -0.4627   0.4279   1.8897  

Coefficients:
                    Estimate Std. Error z value Pr(>|z|)    
(Intercept)           2.0750     0.1683  12.332   <2e-16 ***
treatment2Progabide  -0.4994     0.2397  -2.084   0.0372 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for Negative Binomial(1.4991) family taken to be 1)

    Null deviance: 71.220  on 57  degrees of freedom
Residual deviance: 66.879  on 56  degrees of freedom
AIC: 339.12

Number of Fisher Scoring iterations: 1


              Theta:  1.499 
          Std. Err.:  0.362 

 2 x log-likelihood:  -333.120

Jessi Jessi · Accepted Answer · 2018-07-25T15:24:30

It's the exponential of the sum of the coefficients: seizure.rate2= exp(2.0750-0.4994*treatment2Proabide) =exp(2.075)*exp(-0.4994*treatment2Proabide)

or you can use the code names(YourModelname) This code will give you output of the names and you can look at fitted.values to give you the predicted values. I occasionally do this as a double check to see if I wrote out my formula correctly.

Negative Binomial Regression: coefficient interpretation

1 Answers