over-estimation Negative Binomial models

D_Tomas <tomasmeca <at> hotmail.com> writes:

I have fitted a Negative Binomial model (glm.nb) and a Poisson model (glm
family=poisson) to some count data. Both have the same explanatory variables
& dataset

When I call  sum(fitted(model.poisson))  for my GLM-Poisson model, I obtain
exactly the same number of counts as my data. 

However, when I call sum(fitted(model.neg.binomial)) for my Negative
Binomial model I clearly obtain many more count data (approx 27% more
counts).

Can anyone explain why such stark contrast between the two models exist? Why
is the Negative Binomial massively over-estimating the values? 

Does it have to do with the dispersion parameter of the Negative Binomial
model?

Nothing springs to mind immediately.  Can you post a reproducible
example?

  The trivial example below works:

z <- rpois(1000,5)
pm <- glm(z~1,family=poisson)
sum(fitted(pm))

[1] 4975

sum(z)

[1] 4975

nbm <- MASS::glm.nb(z~1)

Warning messages:
1: In theta.ml(Y, mu, sum(w), w, limit = control$maxit, 
  trace = control$trace >  :
  iteration limit reached
2: In theta.ml(Y, mu, sum(w), w, limit = control$maxit, 
  trace = control$trace >  :
  iteration limit reached

sum(fitted(nbm))

[1] 4975

Ben, 

this is a continuation of the query i posted on: 

http://r.789695.n4.nabble.com/GLM-and-Neg-Binomial-models-td3902173.html

I cannot give you a direct example (big dataset) of what i did aside from
what i have written:
fitpoisson <- glm((RESPONSE) ~ A  + B + 
offset(log(LENGTH)) + offset(log(LENGTH_OBSERVATION)),family="poisson",data=
dataset)  

fitneg <- glm.nb((RESPONSE) ~ A  + B + 
offset(log(LENGTH)) + offset(log(LENGTH_OBSERVATION)),data= dataset)

sum(fitted(fitpoisson))

[1] 373

sum(fitted(fitneg))

[1] 514

Observed data is 373....


Any thoughts?

tomas 

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