Re: model selection problem

Vadim Pliner wrote:

Carsten Steinhoff wrote:

Carsten,

Log Likelihood incorporates probabilities rather than actual values of
x or log(x). Therefore, I cannot see a reason why the Log Likelihood
would get smaller or higher just because you take log of x.

HTH,
Vadim Pliner


Hi Vadim,

so to sum up your posting ... a higher likelihood-value should indicate
a better fit in any way (at least in theory) ?

And an additional question: What I need especially is a good fit in the
right tail of the distribution. Are there modifications to likelihood
criteria to focus more on tail-exactness?

Carsten 

-----------


so to sum up your posting ... a higher likelihood-value should indicate
a better fit in any way (at least in theory) ?



Not necessarily. You also have to take into account the DF's number of
parameters. The higher the value of log likelihood, the better the
distribution function fits the data. However, you cannot simply pick
the one yielding the highest likelihood if the distributions you select
from have different numbers of parameters. Although a higher likelihood
means a better model for the observed data, a higher number of
parameters cause weaker predictability for new cases. It is a good idea
to use either AIC or BIC criteria which you were going to use anyway.


OK. That's my intention. Your text shows me that my initial idea was right.


And an additional question: What I need especially is a good fit in the
right tail of the distribution. Are there modifications to likelihood
criteria to focus more on tail-exactness?



I guess you could assign higher weights to the elements of log
likelihood corresponding to observations in the right tail (longer
lived subjects, if we are talking in the context of survival analysis)
and then maximize this weighted log likelihood.

Does somebody here has an idea HOW to weight the likelihood? I think an exponentiation will work fine for the tail exactness, but maybe somebody has more details or literature? Google research didnt help me further :-(

Tnx, Carsten
.

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