Hi,
thank you for your elaborate answer. I downloaded Prof. Dayton's pdf and
will read it tomorrow.
A friend also told me that our professor said you can actually compare
AICs for different distributions. Apparently it's not correct strictly
speaking, because of the two different likelihoods, but you can get
meaningful information out of it. Did I understand that right?
By the way, what is the etiquette way of answering your post? Should I
mail to you /and/ the list?
Regards,
Alex (with a new e-mail address, in case this mixes something up)
Am 17.03.2011 09:58, schrieb Rubén Roa:
Hi Alexx,
I don't see any problem in comparing models based on different
distributions for the same data using the AIC, as long as they have a
different number of parameters and all the constants are included.
For example, you can compare distribution mixture models with different
number of components using the AIC.
This is one example:
Roa-Ureta. 2010. A Likelihood-Based Model of Fish Growth With Multiple
Length Frequency Data. Journal of Biological, Agricultural and
Environmental Statistics 15:416-429.
Here is another example:
www.education.umd.edu/EDMS/fac/Dayton/PCIC_JMASM.pdf
Prof. Dayton writes above that one advantage of AIC over hypothesis
testing is:
"(d) Considerations related to underlying distributions for random
variables can be
incorporated into the decision-making process rather than being treated
as an assumption whose
robustness must be considered (e.g., models based on normal densities
and on log-normal
densities can be compared)."
Last, if you read Akaike's theorem you will see there is nothing
precluding comparing models built on different distributional models.
Here it is:
" the expected (over the sample space and the space of parameter
estimates) maximum log-likelihood of some data on a working model
overshoots the expected (over the sample space only) maximum
log-likelihood of the data under the true model that
generated the data by exactly the number of parameters in the working
model."
A remarkable result.
Rubén
-----Original Message-----
From: r-help-boun...@r-project.org on behalf of Alexx Hardt
Sent: Wed 3/16/2011 7:42 PM
To: r-help@r-project.org
Subject: Re: [R] R² for non-linear model
Am 16.03.2011 19:34, schrieb Anna Gretschel:
> Am 16.03.2011 19:21, schrieb Alexx Hardt:
>> And to be on-topic: Anna, as far as I know anova's are only useful to
>> compare a submodel (e.g. with one less regressor) to another model.
>>
> thanks! i don't get it either what they mean by fortune...
It's an R-package (and a pdf [1]) with collected quotes from the mailing
list.
Be careful with the suggestion to use AIC. If you wanted to compare two
models using AICs, you need the same distribution (that is,
Verteilungsannahme) in both models.
To my knowledge, there is no way to "compare" a gaussian model to an
exponential one (except common sense), but my knowledge is very limited.
[1] http://cran.r-project.org/web/packages/fortunes/vignettes/fortunes.pdf
--
alexx@alexx-fett:~$ vi .emacs
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