[R] Three-component Negative Binomial Mixture: R code

[Achim Zeileis]

On Tue, 8 Nov 2016, danilo.carita at uniparthenope.it wrote:

> I tried the function flexmix() with the driver FLXMRnegbin() with two 
> components first, in order to compare its results with those provided by my 
> function mixnbinom(). In particular, I ran the following code:
>
>
>> fm0 <- flexmix(y ~ 1, data = data.frame(y), k = 2, model = FLXMRnegbin())
>
>
> where "y" is my vector of counts. The previous function provided me the 
> following parameters:
>
>
>>                   Comp.1   Comp.2
>> coef.(Intercept) 1.2746536 1.788578
>> theta            0.1418201 5.028766
>
>
> with priors 0.342874 and 0.657126, respectively. I assume that the 
> coefficients "Intercept" represent the two means of the model (mu1 and mu2),

No, a log link is employed, i.e., exp(1.2746536) and exp(1.788578) are the 
means.

> while the "theta" coefficients are the size parameters (size1 and size2).

Yes.

> Unfortunately, unlike my function mixnbinom(), the model computed with 
> flexmix() did not provide a good fit to my data (p-value ~0).
>
> Is there something wrong in the process above?

Hard to say without a reproducible example. Using parameter values similar 
to the ones you cite above, the following seems to do a reasonable job:

## packages
library("countreg")
library("flexmix")

## artificial data from two NB distributions:
## 1/3 is NB(mu = 3.5, theta = 0.2) and
## 2/3 is NB(mu = 6.0, theta = 5.0)
set.seed(1)
y <- c(rnbinom(200, mu = 3.5, size = 0.2), rnbinom(400, mu = 6, size = 5))

## fit 2-component mixture model
set.seed(1)
fm <- flexmix(y ~ 1, k = 2, model = FLXMRnegbin())

## inspect estimated parameters -> look acceptable
parameters(fm)
exp(parameters(fm)[1,])

My experience was that finding good starting values may be a problem for 
flexmix(). So maybe setting these in some better way would be beneficial.

> Achim Zeileis <Achim.Zeileis at uibk.ac.at> ha scritto:
>
>> On Mon, 7 Nov 2016, danilo.carita at uniparthenope.it wrote:
>> 
>>> I need a function for R software which computes a mixture of Negative
>>> Binomial distributions with at least three components.
>> 
>> The package "countreg" on R-Forge provides a driver FLXMRnegbin() that can 
>> be combined with the "flexmix" package (i.e., functions flexmix() and 
>> stepFlexmix()). The manual page provides some worked illustrations in 
>> example("FLXMRnegbin", package = "countreg").
>> 
>> Note that the driver is mainly designed for negative binomial _regression_ 
>> models. But if you just regress on a constant (y ~ 1) you can also get 
>> negative binomial mixture distributions without covariates.
>
>
> -------------------------------------------------------------
> Danilo Carità
>
> PhD Candidate
> University of Naples "Parthenope"
> Dipartimento di Studi Aziendali e Quantitativi
> via G. Parisi, 13, 80132 Napoli - Italy
> -------------------------------------------------------------
>