[R] negative binomial family glm R and STATA

[Mikis Stasinopoulos]

Dear  Patrick

Try the package gamlss which allow to fit the negative binomial 
distrbution. For example  with your data I am getting
#---------------------------------------------------
ga1<-gamlss(nbcas~.,data=zonesdb4,family=NBI)
GAMLSS-RS iteration 1: Global Deviance = 817.9027
GAMLSS-RS iteration 2: Global Deviance = 817.9025
 ga1

Family:  c("NBI", "Negative Binomial type I")
Fitting method: RS()

Call:  gamlss(formula = nbcas ~ ., family = NBI, data = zonesdb4)

Mu Coefficients:
 (Intercept)           pop          Area    V_100kHab1        gares1 
   3.204e+00     1.114e-05     1.354e-05     9.144e-01     7.946e-01 
      ports1  axe_routier1  axe_routier2         lacs1 
  -1.730e+00     1.989e-01            NA     3.042e+00 
Sigma Coefficients:
(Intercept) 
      2.313 

 Degrees of Freedom for the fit: 9 Residual Deg. of Freedom   83
Global Deviance:     817.902
            AIC:     835.902
            SBC:     858.599
#--------------------------------------------------------------

Note that the AIC: 835.902 is similar to your fitted model using  glm.nb 
which is  AIC: 836.2.

The coefficients are not identical but this is not suprissing when you 
are using x-variables with extreme values as pop and Area.
The profile function for sigma can be found using

prof.dev(ga1,"sigma", min=7, max=16, step=0.1, type="l")

Your discrepancy with STATA come from the fact that in STATA you are 
fitting the model with sigma fixed to 1.
You can see that by fitting the same model in  GAMLSS.

 >  ga2<-gamlss(nbcas~.,data=zonesdb4,family=NBI, sigma.fix=T, 
sigma.start=1)
GAMLSS-RS iteration 1: Global Deviance = 1194.299
GAMLSS-RS iteration 2: Global Deviance = 1194.298

This  is similar  to  the  log likelihod you are  getting in STATA. i.e. 
-2*-597.14778= 1194.296.

You can also use the stepGAIC() function to simplify your model. For  
example

 ga2<-stepGAIC(ga1)

will result to a model with only pop and lacs in the mdel.

Note also the the Negative binomial type II fits better to you data.

 >  ga3<-gamlss(nbcas~.,data=zonesdb4,family=NBII)
GAMLSS-RS iteration 1: Global Deviance = 804.5682
...
GAMLSS-RS iteration 10: Global Deviance = 804.4995


Thanks

Mikis