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

[danilo.carita at uniparthenope.it]

Thank you for your hints, now the goodness of fit test provides me  
good results, but surprisingly for me the three-component model turns  
out to be worse than the two-component one (indeed, I focused on the  
three-component mixture because the two-component one exhibits a low  
p-value).

In addition, I have noticed that for some data the function fails to  
find good starting values, as you have mentioned in your previuous  
answer. The problem is that the driver FLXMRnegbin() allows to specify  
only the theta parameter (and only one value, even in the event of  
mixtures of two or more components).

I have read the description of flexmix() function too, but it seems  
that it does not allow to set starting values for the parameters of  
the model. Am I right? Or is there a way to do it?




Achim Zeileis <Achim.Zeileis a uibk.ac.at> ha scritto:

> On Tue, 8 Nov 2016, danilo.carita a 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.



-------------------------------------------------------------
Danilo Carità

PhD Candidate
University of Naples "Parthenope"
Dipartimento di Studi Aziendali e Quantitativi
via G. Parisi, 13, 80132 Napoli - Italy