On Wednesday 25 June 2003 20:23, 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 > > The difference in this simple example is slight, but > it is magnified when using my data.
That is because you are not using the ML estimate of the variance. sigmaML <- sqrt(mean(residuals(test.lm)^2)) sum(dnorm(y, y.hat, sigmaML, log=T)) # [1] -57.20699 Best, Z > My understanding is > that it is necessary to use the complete likelihood functions > for both the Gamma model and the 'lognormal' model (no constants > removed, etc.) in order to accurately compare using AIC. > > Can someone point out my error, or explain this discrepancy? > > Thanks in advance! > > ______________________________________________ > [EMAIL PROTECTED] mailing list > https://www.stat.math.ethz.ch/mailman/listinfo/r-help ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help
