I have fit a GLM poisson regression model. Then i detected overdispersion, which was the reason that I have decided to fit a Negative Binomial model:
# oversidpersion check
dispersiontest(poismodel, trafo = 0)
dispersiontest(poismodel.t, trafo = 0)
# there is evidence of overdispersion (c is estimated to be 18.13873) which speaks quite strongly
# against the assumption of equidispersion (i.e. c=0).
summary(ngbinomial)
ngbinomial.t <-glm.nb(TOT.N ~ OPEN.L + sqrt(MONT.S) + sqrt(POLIC) + D.PARK + sqrt(SHRUB) +
sqrt(WAT.RES) + L.WAT.C + sqrt(L.P.ROAD) + D.WAT.COUR)
summary(ngbinomial.t)
# conclusion : negative binomial is great improvement over the poisson model (based on AIC)
I have then run a (manual) stepwise selection procedure using add1
and drop1
, as well as automatic selection procedure stepAIC
.
Is it ok to run the stepwise selection procedure on the negative binomial model? does this procedure need to be adjusted?
(The corresponding output for my selection procedure – just the last step is included):
BACKWARD SELECTION:
> nbmodel <- glm.nb(TOT.N ~ OPEN.L + sqrt(MONT.S) + sqrt(POLIC) + D.PARK +
+ sqrt(SHRUB) + L.WAT.C + sqrt(L.P.ROAD) + D.WAT.COUR)
> back <- stepAIC(nbmodel, direction = "backward")
Start: AIC=386.94
TOT.N ~ OPEN.L + sqrt(MONT.S) + sqrt(POLIC) + D.PARK + sqrt(SHRUB) +
L.WAT.C + sqrt(L.P.ROAD) + D.WAT.COUR
Step: AIC=381.54
TOT.N ~ OPEN.L + D.PARK + L.WAT.C + sqrt(L.P.ROAD)
Df AIC
<none> 381.54
- sqrt(L.P.ROAD) 1 382.25
- L.WAT.C 1 383.42
- OPEN.L 1 390.82
- D.PARK 1 443.91
BACKWARD + FORWARD SELECTION:
> both <- stepAIC(nbmodel, direction = "both")
Start: AIC=386.94
TOT.N ~ OPEN.L + sqrt(MONT.S) + sqrt(POLIC) + D.PARK + sqrt(SHRUB) +
L.WAT.C + sqrt(L.P.ROAD) + D.WAT.COUR
Step: AIC=381.54
TOT.N ~ OPEN.L + D.PARK + L.WAT.C + sqrt(L.P.ROAD)
Df AIC
<none> 381.54
+ sqrt(MONT.S) 1 382.25
- sqrt(L.P.ROAD) 1 382.25
+ sqrt(POLIC) 1 383.04
+ D.WAT.COUR 1 383.38
- L.WAT.C 1 383.42
+ sqrt(SHRUB) 1 383.50
- OPEN.L 1 390.82
- D.PARK 1 443.91
Or would you advice me to first run the selection procedure on the poisson model and then fit a negative binomial model on the already reduced poisson model ?
Best Answer
You should not do stepwise regression or any similar approaches whether based on p-values or AIC or anything else (most certainly not without adjusting the final inferences for it), see e.g. Algorithms for automatic model selection. Whether you are looking at a Poisson or a negatie binomial model does not affect this answer, at all.
Approaches like LASSO/elastic net (with cross-validation) or Bayesian shrinkage priors (e.g. the horseshoe, easily available e.g. in rstanarm) are generally preferrable.