Solved – How to interpret a negative binomial regression with categorical predictor

negative-binomial-distributionregression coefficients

I am trying to interpret R output for a negative binomial regression.

Below is my output. I'm trying to infer how much my predictor (socfrend_bin) affects my response (union_d), but looking at my predictor as a categorical, rather than continuous, variable.

How should I interpret these coefficients? I am currently interpreting this as e^coefficient = the number of times greater probability of union_d == 1, as opposed to 0. Please help!?

`Call:
glm.nb(formula = union_d ~ factor(socfrend_bin) + male, data = selected %>% 
    filter(YEAR == 2016), init.theta = 1860.745148, link = log)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-0.5479  -0.4571  -0.4140  -0.3343   2.1378  

Coefficients:
                          Estimate Std. Error z value Pr(>|z|)    
(Intercept)                -3.2464     0.3635  -8.932   <2e-16 ***
factor(socfrend_bin)3       0.3616     0.4217   0.858   0.3912    
factor(socfrend_bin)4       0.7896     0.3888   2.031   0.0422 *  
factor(socfrend_bin)5       0.9019     0.3932   2.294   0.0218 *  
factor(socfrend_bin)6 & 7   0.5393     0.4221   1.278   0.2014    
male                        0.4482     0.2229   2.010   0.0444 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for Negative Binomial(1860.745) family taken to be 1)

    Null deviance: 419.54  on 969  degrees of freedom
Residual deviance: 407.54  on 964  degrees of freedom
AIC: 595.59

Number of Fisher Scoring iterations: 1


              Theta:  1861 
          Std. Err.:  14675 
Warning while fitting theta: iteration limit reached 

 2 x log-likelihood:  -581.588`

Best Answer

I think your interpretation is correct.

I often find that the best way to get a sense of what is going on is to look at predicted values of the dependent variable for different combinations of the independent variables. In your case, there are only two IVs, and not that many levels, so you could look at all combinations of (male/female) and (socfrend).

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