Please try to read the whole paragraph. When you have done that, read my exposition in my PRNN book.
Hint 1: AIC is about maximized likelihood, and one of the models being compared is not being fitted by ML. Hint 2: Differences in AIC for non-nested models are subject to large sampling fluctuations (and Mr Dick was worrying about differences of the order of 0.06). On Fri, 27 Jun 2003, Ravi Varadhan wrote: > This is not a typical R posting, but I was quite surprised to read > Prof. Ripley's comment about the inappropriate use of AIC to > compare "non-nested" models. As he says, While it is indeed true that > Akaike's (1973) develops AIC for nested models, i.e. models which can > be obtained by various restrictions on parameters, it is not at all > obvious to me that it can't be used for non-nested cases. That it is not obvious to you does not make it true. You have to prove that methods work, not that they don't work (a common mistake). > To quote Stone (1977, JRSS B): "Akaike's derivation of AIC was for > heirarchical models but, as he finally remarked, this restriction is > unnecessary." I don't know where Akaike made this remark - I couldn't > see it in his 1973 paper - but AIC has indeed been used in various > situations where the models are non-nested. From the motivation of AIC > as an unbiased estimator of the Kullback-Leibler divergence of asssumed > model from the "true" model, it is not clear that the models have to be > nested. > > Any thoughts or comments on this issue? > > Best, > Ravi. > > > ----- Original Message ----- > From: Prof Brian Ripley <[EMAIL PROTECTED]> > Date: Wednesday, June 25, 2003 2:59 pm > Subject: Re: [R] logLik.lm() > > > Your by-hand calculation is wrong -- you have to use the MLE of > > sigma^2. > > sum(dnorm(y, y.hat, sigma * sqrt(16/18), log=TRUE)) > > > > Also, this is an inappropriate use of AIC: the models are not > > nested, and > > Akaike only proposed it for nested models. Next, the gamma GLM is > > not a > > maximum-likelihood fit unless the shape parameter is known, so you > > can'tuse AIC with such a model using the dispersion estimate of shape > > > > The AIC output from glm() is incorrect (even in that case, since the > > shape is always estimated by the dispersion). > > > > On Wed, 25 Jun 2003, Edward Dick wrote: > > > > > Hello, > > > > > > I'm trying to use AIC to choose between 2 models with > > > positive, continuous response variables and different error > > > distributions (specifically a Gamma GLM with log link and a > > > normal linear model for log(y)). I understand that in some > > > cases it may not be possible (or necessary) to discriminate > > > between these two distributions. However, for the normal > > > linear model I noticed a discrepancy between the output of > > > the AIC() function and my calculations done "by hand." > > > This is due to the output from the function logLik.lm(), > > > which does not match my results using the dnorm() function > > > (see simple regression example below). > > > > > > x <- c(43.22,41.11,76.97,77.67,124.77,110.71,144.46,188.05,171.18, > > > > > 204.92,221.09,178.21,224.61,286.47,249.92,313.19,332.17,374.35)> y > > <- c(5.18,12.47,15.65,23.42,27.07,34.84,31.03,30.87,40.07,57.36, > > > 47.68,43.40,51.81,55.77,62.59,66.56,74.65,73.54) > > > test.lm <- lm(y~x) > > > y.hat <- fitted(test.lm) > > > sigma <- summary(test.lm)$sigma > > > logLik(test.lm) > > > # `log Lik.' -57.20699 (df=3) > > > sum(dnorm(y, y.hat, sigma, log=T)) > > > # [1] -57.26704 > > > > -- > > Brian D. Ripley, [EMAIL PROTECTED] > > Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ > > University of Oxford, Tel: +44 1865 272861 (self) > > 1 South Parks Road, +44 1865 272866 (PA) > > Oxford OX1 3TG, UK Fax: +44 1865 272595 > > > > ______________________________________________ > > [EMAIL PROTECTED] mailing list > > https://www.stat.math.ethz.ch/mailman/listinfo/r-help > > > > -- Brian D. Ripley, [EMAIL PROTECTED] Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595 ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help
