[R] test the goodness of it for negative binomial type 2

[Achim Zeileis]

On Tue, 2 Mar 2010, casperyc wrote:

>
> [code]library(MASS)
> x=c(rep(0,8096),
>        rep(1,1629),
>        rep(2,233),
>        rep(3,38),
>        rep(4,4)
>        )
>
> x.bar=round(mean(x),4)
> x.var=round(var(x),4)
>
> p.hat=round(x.bar/x.var,4)
> alpha.hat=round(x.bar*p.hat/(1-p.hat),4)
>
> fitdistr(x, "Negative Binomial")
> fitdistr(x, "Poisson")[/code]
>
>
> 1- fitdistr(x, "Negative Binomial")
>   the parameters got here, is it for negative binomial type 2?

Yes.

>   how can i ask it to use the methods of moments to calculat the
> parameters?

You can't with fitdist()

>   (p.hat and alpha.hat which i derived from methods of moments seem to give
> a different value)

It is a different parametrization of NB2 that you are using. Your 
alpha.hat corresponds to "size" and p.hat corresponds to "prob" in 
?dnbinom. However, fitdistr() uses the "mu" parametrization, i.e.

R> alpha.hat * (1 - p.hat) / p.hat
[1] 0.222497

which roughly matches the ML estimate for mu from fitdistr().

> 2-how can i fit it and than test the goodness of it?

You could use goodfit() from "vcd":

gf_pois <- goodfit(x, type = "poisson")
plot(gf_pois)
summary(gf_pois)

gf_nbin <- goodfit(x, type = "nbinom")
plot(gf_nbin)
summary(gf_nbin)

which shows that the fit from the NB is satisfactory while the fit from 
the Poisson is not.

hth,
Z

> 3-then compare with the Poisson model?
>
> Thanks
>
> ===============================================
>
> by negative binomial type two i mean
>
>
>
>
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