Re: [R] How to read the summary
On Tue, 28 Apr 2009, K. Elo wrote: mathallan wrote: How can I from the summary function, decide which glm (fit1, fit2 or fit3) fits to data best? I don't know what to look after, so I would please explain the important output. Start with the AIC value (Akaike Information Criterion). The model having the lowest AIC is the best (of the fitted models, of course). So, in Your case, the AICs are: fit1 - glm(Y~X, family=gaussian(link=identity)) AIC: 51.294 fit2 - glm(Y~X, family=gaussian(link=log)) AIC: 32.954 fit3 - glm(Y~X, family=Gamma(link=log)) AIC: 36.65 Hence, the best model seems to be 'fit2'. Except that fit3 did not use maximum likelihood to estimate the shape parameter and so that is not really a valid AIC value (and the actual AIC will be smaller since the maximized likelihood will be larger). Given that, and that AIC differences between non-nested models are highly variable I would see no clearcut difference between fit2 and fit3. (Even for nested models an AIC difference of not more than 3.7 would not be seen as a large difference.) This is not really about the subject line at all: 'AIC' as printed here is computed by glm() and not summary.glm(). There is a warning about it on the ?glm help page (all the 'AIC' values quoted here do not take account of the estimation of the dispersion parameter), and AIC() does a slightly better job. -- Brian D. Ripley, rip...@stats.ox.ac.uk 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, UKFax: +44 1865 272595 __ 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.
[R] How to read the summary
How can I from the summary function, decide which glm (fit1, fit2 or fit3) fits to data best? I don't know what to look after, so I would please explain the important output. fit1 - glm(Y~X, family=gaussian(link=identity)) fit2 - glm(Y~X, family=gaussian(link=log)) fit3 - glm(Y~X, family=Gamma(link=log)) summary(fit1) Call: glm(formula = Y ~ X, family = gaussian(link = identity)) Deviance Residuals: Min 1Q Median 3Q Max -3.6619 -1.9693 -0.4119 2.0787 3.9664 Coefficients: Estimate Std. Error t value Pr(|t|) (Intercept) -0.4285 1.6213 -0.264 0.798258 X 4.3952 0.7089 6.200 0.000259 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for gaussian family taken to be 6.784605) Null deviance: 315.081 on 9 degrees of freedom Residual deviance: 54.277 on 8 degrees of freedom AIC: 51.294 Number of Fisher Scoring iterations: 2 summary(fit2) Call: glm(formula = Y ~ X, family = gaussian(link = log)) Deviance Residuals: Min 1Q Median 3Q Max -1.5489 -0.2960 0.4776 0.6353 1.2773 Coefficients: Estimate Std. Error t value Pr(|t|) (Intercept) 0.505370.16562 3.051 0.0158 * X0.663520.05083 13.055 1.13e-06 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for gaussian family taken to be 1.083989) Null deviance: 315.0810 on 9 degrees of freedom Residual deviance: 8.6718 on 8 degrees of freedom AIC: 32.954 Number of Fisher Scoring iterations: 6 summary(fit3) Call: glm(formula = Y ~ X, family = Gamma(link = log)) Deviance Residuals: Min1QMedian3Q Max -0.35269 -0.09272 0.02550 0.13625 0.18018 Coefficients: Estimate Std. Error t value Pr(|t|) (Intercept) 0.859590.11244 7.645 6.04e-05 *** X0.531340.04916 10.808 4.74e-06 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for Gamma family taken to be 0.03262828) Null deviance: 4.31315 on 9 degrees of freedom Residual deviance: 0.28385 on 8 degrees of freedom AIC: 36.65 Number of Fisher Scoring iterations: 5 -- View this message in context: http://www.nabble.com/How-to-read-the-summary-tp23276848p23276848.html Sent from the R help mailing list archive at Nabble.com. __ 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.
Re: [R] How to read the summary
Hi! mathallan wrote: How can I from the summary function, decide which glm (fit1, fit2 or fit3) fits to data best? I don't know what to look after, so I would please explain the important output. Start with the AIC value (Akaike Information Criterion). The model having the lowest AIC is the best (of the fitted models, of course). So, in Your case, the AICs are: fit1 - glm(Y~X, family=gaussian(link=identity)) AIC: 51.294 fit2 - glm(Y~X, family=gaussian(link=log)) AIC: 32.954 fit3 - glm(Y~X, family=Gamma(link=log)) AIC: 36.65 Hence, the best model seems to be 'fit2'. Kind regards, Kimmo __ 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.
