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 ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. [[alternative HTML version deleted]]
______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
