7.5 Negative Binomial Regression

library(MASS)
NegBinom_Mod <- MASS::glm.nb(Num_Article ~ .,bioChemists)
summary(NegBinom_Mod)
#> 
#> Call:
#> MASS::glm.nb(formula = Num_Article ~ ., data = bioChemists, init.theta = 2.264387695, 
#>     link = log)
#> 
#> Deviance Residuals: 
#>     Min       1Q   Median       3Q      Max  
#> -2.1678  -1.3617  -0.2806   0.4476   3.4524  
#> 
#> Coefficients:
#>                  Estimate Std. Error z value Pr(>|z|)    
#> (Intercept)      0.256144   0.137348   1.865 0.062191 .  
#> SexWomen        -0.216418   0.072636  -2.979 0.002887 ** 
#> MarriedMarried   0.150489   0.082097   1.833 0.066791 .  
#> Num_Kid5        -0.176415   0.052813  -3.340 0.000837 ***
#> PhD_Quality      0.015271   0.035873   0.426 0.670326    
#> Num_MentArticle  0.029082   0.003214   9.048  < 2e-16 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> (Dispersion parameter for Negative Binomial(2.2644) family taken to be 1)
#> 
#>     Null deviance: 1109.0  on 914  degrees of freedom
#> Residual deviance: 1004.3  on 909  degrees of freedom
#> AIC: 3135.9
#> 
#> Number of Fisher Scoring iterations: 1
#> 
#> 
#>               Theta:  2.264 
#>           Std. Err.:  0.271 
#> 
#>  2 x log-likelihood:  -3121.917

We can see the dispersion is 2.264 with SE = 0.271, which is significantly different from 1, indicating over-dispersion. Check Over-Dispersion for more detail