The contribution of each observation to the logliklihood is
log(p*f1(x) + (1-p)*f2(x))
where f1 and f2 are the two density functions. Just sum.
The standard likelihood ratio test is problematic here, as there
are two parametrizations that reduce the mixture model to a single
component: p=1 vs p < 1 plus the shape and scale parameters
of the two components are identical.
albyn
On 3/5/12 2:57 AM, n.albe...@roehampton.ac.uk wrote:
Hello,
I would like to fit a mixture of two Weibull distributions to my
data, estimate the model parameters, and compare the fit of the model
to that of a single Weibull distribution.
I have used the mix() function in the 'mixdist' package to fit the
mixed distribution, and have got the parameter estimates, however, I
have not been able to get the log-likelihood for the fit of this
model
in order to compare it to the single distribution.
I have also had a look at the 'Mixtools' and 'Flexmix' packages. With
both of these it is possible to fit a mixture of distributions, but,
as far as I can tell, these are pre-defined and do not have a
function
for a mixture of two Weibull distributions.
I have used the 'fitdistrplus' package to fit the single
distribution.
Does anyone have any suggestions either for getting the
log-likelihood for models fitted with the mix() function, or other
packages / functions which allow me to fit a double Weibull and get
the log-likelihood for the model?
Any suggestions are much appreciated!
Best wishes,
Nienke
----------------------------------------------------------------------------------------------
Nienke Alberts
PhD Candidate
Centre of Research in Evolutionary & Environmental Anthropology
University of Roehampton
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