[R] Number of components in a mixture model

[Christian Hennig]

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
> 
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***********************************************************************
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/
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