R help - Jul 2003 - Number of components in a mixture model

Dear all,

I'm fitting a set of length-of-stay data by a model of mixture of 
exponentials. I've been following the example on page 436 in MASS (5th Ed.).
However, I have a couple of questions while following this example.

What if we don't know how many components there are in the model in advance.
Is there any established method to determine the number of components from a 
set of data? I'm aware that the usual likelihood ratio test is not 
appropriate in this case due to the possibility that the ML could occur at 
the boundry of the parameter space.

Secondly, the example in MASS uses a Q-Q plot to informally assess GOF. I 
was wondering if there are some more formal statistical tests for this 
purpose.

I appologise for asking questions that are slightly out-of-topic.

Many thanks.

Kevin

Hi Kevin,

a more or less established method (at least for normal mixtures) is the use of
the Bayesian information criterion BIC defined as maximization of 
2* max loglikelihood (s) -log(n)*number of fitted parameters for model s,
s being the number of components, n number of points, over s. 
However I have no experience with it in connection with exponential mixtures.

Christian

On Wed, 30 Jul 2003, kevin xie wrote:
> Dear all,
> 
> I'm fitting a set of length-of-stay data by a model of mixture of 
> exponentials. I've been following the example on page 436 in MASS (5th
Ed.).
> However, I have a couple of questions while following this example.
> 
> What if we don't know how many components there are in the model in
advance.
> Is there any established method to determine the number of components from
a
> set of data? I'm aware that the usual likelihood ratio test is not 
> appropriate in this case due to the possibility that the ML could occur at 
> the boundry of the parameter space.
> 
> Secondly, the example in MASS uses a Q-Q plot to informally assess GOF. I 
> was wondering if there are some more formal statistical tests for this 
> purpose.
> 
> I appologise for asking questions that are slightly out-of-topic.
> 
> Many thanks.
> 
> Kevin
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help
> 
***********************************************************************
Christian Hennig
Seminar fuer Statistik, ETH-Zentrum (LEO), CH-8092 Zuerich (current)
and Fachbereich Mathematik-SPST/ZMS, Universitaet Hamburg
hennig at stat.math.ethz.ch, http://stat.ethz.ch/~hennig/
hennig at math.uni-hamburg.de, http://www.math.uni-hamburg.de/home/hennig/
#######################################################################
ich empfehle www.boag.de