From: Ruben Roa <RRoa_at_fisheries.gov.fk>

Date: Tue 21 Feb 2006 - 22:26:15 EST

Hi, Aaron, Burnham & Anderson are explicit but they do not go into any depth regarding this issue. Akaike's colleagues Sakamoto, Ishiguro, and Kitagawa (Akaike Information Criterion Statistics, 1986, KTK Scientific Publishers) do no either, deal with it directly, and the examples they present that I have examined (not even half of the total in the book), are all of nested models. However, by reading some of Akaike's papers and the book quoted above it does not appear to me that there is any restriction on the use of the AIC related to nestedness. In fact, the theory does not preclude the comparison of models with different *probability densities (or mass)* as long as you keep all constants (like 1/sqrt(2pi) in the normal) in the calculation. Akaike (1973) wrote in the first sentence of his paper his general principle, which he called an extension of the maximum likelihood principle: "Given a set of estimates theta_hat's of the vector of parameters theta of a probability distribution with density f(x|theta) we adopt as our final estimate the one which will give the maximum of the expected log-likelihood, which is by definition E(log f(X|theta_hat))=E(INTEGRAL f(x|theta)log f(x|theta_hat)dx) Where X is a random variable following the distribution with the density function f(x|theta) and is independent of theta_hat". All subsequent derivations in the paper, like the choice of distance measure, class of estimates, and elimination of the true parameter value, revolve around this principle. Now, nestedness is a mathematical property of what Burnham & Anderson call "the structural model", whereas Akaike's principle only concerns the probabilistic model f(x|theta) where the structural model is embedded. I reply to you even though I do not feel strongly about this issue and you asked for replies from people who feel strongly about this issue. Ruben

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue Feb 21 23:30:59 2006

Date: Tue 21 Feb 2006 - 22:26:15 EST

Hi, Aaron, Burnham & Anderson are explicit but they do not go into any depth regarding this issue. Akaike's colleagues Sakamoto, Ishiguro, and Kitagawa (Akaike Information Criterion Statistics, 1986, KTK Scientific Publishers) do no either, deal with it directly, and the examples they present that I have examined (not even half of the total in the book), are all of nested models. However, by reading some of Akaike's papers and the book quoted above it does not appear to me that there is any restriction on the use of the AIC related to nestedness. In fact, the theory does not preclude the comparison of models with different *probability densities (or mass)* as long as you keep all constants (like 1/sqrt(2pi) in the normal) in the calculation. Akaike (1973) wrote in the first sentence of his paper his general principle, which he called an extension of the maximum likelihood principle: "Given a set of estimates theta_hat's of the vector of parameters theta of a probability distribution with density f(x|theta) we adopt as our final estimate the one which will give the maximum of the expected log-likelihood, which is by definition E(log f(X|theta_hat))=E(INTEGRAL f(x|theta)log f(x|theta_hat)dx) Where X is a random variable following the distribution with the density function f(x|theta) and is independent of theta_hat". All subsequent derivations in the paper, like the choice of distance measure, class of estimates, and elimination of the true parameter value, revolve around this principle. Now, nestedness is a mathematical property of what Burnham & Anderson call "the structural model", whereas Akaike's principle only concerns the probabilistic model f(x|theta) where the structural model is embedded. I reply to you even though I do not feel strongly about this issue and you asked for replies from people who feel strongly about this issue. Ruben

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue Feb 21 23:30:59 2006

*
This archive was generated by hypermail 2.1.8
: Fri 03 Mar 2006 - 03:42:38 EST
*