With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

Negative binomial errors

Instead of using quasi-Poisson errors (as above) we could use a negative binomial model. This is in the MASS library and involves the function glm.nb. The modelling proceeds in exactly the same way as with a typical GLM:

```model.nb1<-glm.nb(Days~Eth*Sex*Age*Lrn)
summary(model.nb1,cor=F)

Call:
glm.nb(formula = Days ~ Eth * Sex * Age * Lrn, init.theta =

(DispersionparameterforNegativeBinomial(1.9284)family taken to be 1)

Null deviance: 272.29 on 145 degrees of freedom
Residual deviance: 167.45 on 118 degrees of freedom
AIC: 1097.3

Theta: 1.928
Std. Err.: 0.269
2 x log-likelihood: -1039.324```

The output is slightly different than a conventional GLM: you see the estimated negative binomial parameter (here called theta, but known to us as k and equal to 1.928) and its approximate standard error (0.269) and 2 times the log-likelihood (contrast this with the residual deviance from our quasi-Poisson model, which was 1301.1; see above). Note that the residual deviance in the negative binomial model (167.45) is not 2 times the log-likelihood.

An advantage of the negative binomial model over the quasi-Poisson is that we can automate the model simplification with stepAIC:

```model.nb2<-stepAIC(model.nb1)
summary(model.nb2,cor=F) Coefficients: (3 not defined because of singularities) Estimate Std. Error z value Pr(>|z|) (Intercept) 3.1693 0.3411 9.292 < 2e-16 *** EthN -0.3560 0.4210 -0.845 0.397848 SexM -0.6920 0.4138 -1.672 0.094459 . AgeF1 ...```

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required