Thank you everyone for your help, but my introduction to GAM is turning my brain to mush. I thought the one part of the output I understood the best was r-sq (adj), but now even this is becoming foggy.
In my original message I mentioned a gam fit that turns out to be a linear fit. By curiosity I analysed it with a linear predictor only with mgcv package, and then as a linear model. The output was identical in both, but the r-sq (adj) was 0.55 in mgcv and 0.26 in lm. In lm I hope that my interpretation that 26% of the variance in y is explained by the linear relationship with x is valid. Then what does r2 mean in mgcv? Denis > summary.gam(lin) Family: gaussian Link function: identity Formula: wm.sed ~ Temp Parametric coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.162879 0.019847 8.207 1.14e-09 *** Temp -0.023792 0.006369 -3.736 0.000666 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 R-sq.(adj) = 0.554 Deviance explained = 28.5% GCV score = 0.09904 Scale est. = 0.093686 n = 37 > summary(sed.true.lin) Call: lm(formula = wm.sed ~ Temp, weights = N.sets) Residuals: Min 1Q Median 3Q Max -0.6138 -0.1312 -0.0325 0.1089 1.1449 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.162879 0.019847 8.207 1.14e-09 *** Temp -0.023792 0.006369 -3.736 0.000666 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.3061 on 35 degrees of freedom Multiple R-Squared: 0.285, Adjusted R-squared: 0.2646 F-statistic: 13.95 on 1 and 35 DF, p-value: 0.000666 Le 05-10-05 à 09:45, John Fox a écrit : > Dear Denis, > > Take a closer look at the anova table: The models provide identical > fits to > the data. The differences in degrees of freedom and deviance > between the two > models are essentially zero, 5.5554e-10 and 2.353e-11 respectively. > > I hope this helps, > John > > -------------------------------- > John Fox > Department of Sociology > McMaster University > Hamilton, Ontario > Canada L8S 4M4 > 905-525-9140x23604 > http://socserv.mcmaster.ca/jfox > -------------------------------- > > >> -----Original Message----- >> From: [EMAIL PROTECTED] >> [mailto:[EMAIL PROTECTED] On Behalf Of Denis Chabot >> Sent: Wednesday, October 05, 2005 8:22 AM >> To: r-help@stat.math.ethz.ch >> Subject: [R] testing non-linear component in mgcv:gam >> >> Hi, >> >> I need further help with my GAMs. Most models I test are very >> obviously non-linear. Yet, to be on the safe side, I report >> the significance of the smooth (default output of mgcv's >> summary.gam) and confirm it deviates significantly from linearity. >> >> I do the latter by fitting a second model where the same >> predictor is entered without the s(), and then use anova.gam >> to compare the two. I thought this was the equivalent of the >> default output of anova.gam using package gam instead of mgcv. >> >> I wonder if this procedure is correct because one of my >> models appears to be linear. In fact mgcv estimates df to be >> exactly 1.0 so I could have stopped there. However I >> inadvertently repeated the procedure outlined above. I would >> have thought in this case the anova.gam comparing the smooth >> and the linear fit would for sure have been not significant. >> To my surprise, P was 6.18e-09! >> >> Am I doing something wrong when I attempt to confirm the non- >> parametric part a smoother is significant? Here is my example >> case where the relationship does appear to be linear: >> >> library(mgcv) >> >>> This is mgcv 1.3-7 >>> >> Temp <- c(-1.38, -1.12, -0.88, -0.62, -0.38, -0.12, 0.12, >> 0.38, 0.62, 0.88, 1.12, >> 1.38, 1.62, 1.88, 2.12, 2.38, 2.62, 2.88, 3.12, >> 3.38, 3.62, 3.88, >> 4.12, 4.38, 4.62, 4.88, 5.12, 5.38, 5.62, 5.88, >> 6.12, 6.38, 6.62, 6.88, >> 7.12, 8.38, 13.62) >> N.sets <- c(2, 6, 3, 9, 26, 15, 34, 21, 30, 18, 28, 27, 27, >> 29, 31, 22, 26, 24, 23, >> 15, 25, 24, 27, 19, 26, 24, 22, 13, 10, 2, 5, 3, >> 1, 1, 1, 1, 1) wm.sed <- c(0.000000000, 0.016129032, >> 0.000000000, 0.062046512, 0.396459596, 0.189082949, >> 0.054757925, 0.142810440, 0.168005168, >> 0.180804428, 0.111439628, 0.128799505, >> 0.193707937, 0.105921610, 0.103497845, >> 0.028591837, 0.217894389, 0.020535469, >> 0.080389068, 0.105234450, 0.070213450, >> 0.050771363, 0.042074434, 0.102348837, >> 0.049748344, 0.019100478, 0.005203125, >> 0.101711864, 0.000000000, 0.000000000, >> 0.014808824, 0.000000000, 0.222000000, >> 0.167000000, 0.000000000, 0.000000000, >> 0.000000000) >> >> sed.gam <- gam(wm.sed~s(Temp),weight=N.sets) >> summary.gam(sed.gam) >> >>> Family: gaussian >>> Link function: identity >>> >>> Formula: >>> wm.sed ~ s(Temp) >>> >>> Parametric coefficients: >>> Estimate Std. Error t value Pr(>|t|) >>> (Intercept) 0.08403 0.01347 6.241 3.73e-07 *** >>> --- >>> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 >>> >>> Approximate significance of smooth terms: >>> edf Est.rank F p-value >>> s(Temp) 1 1 13.95 0.000666 *** >>> --- >>> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 >>> >>> R-sq.(adj) = 0.554 Deviance explained = 28.5% >>> GCV score = 0.09904 Scale est. = 0.093686 n = 37 >>> >> >> # testing non-linear contribution >> sed.lin <- gam(wm.sed~Temp,weight=N.sets) >> summary.gam(sed.lin) >> >>> Family: gaussian >>> Link function: identity >>> >>> Formula: >>> wm.sed ~ Temp >>> >>> Parametric coefficients: >>> Estimate Std. Error t value Pr(>|t|) >>> (Intercept) 0.162879 0.019847 8.207 1.14e-09 *** >>> Temp -0.023792 0.006369 -3.736 0.000666 *** >>> --- >>> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 >>> >>> >>> R-sq.(adj) = 0.554 Deviance explained = 28.5% >>> GCV score = 0.09904 Scale est. = 0.093686 n = 37 >>> >> anova.gam(sed.lin, sed.gam, test="F") >> >>> Analysis of Deviance Table >>> >>> Model 1: wm.sed ~ Temp >>> Model 2: wm.sed ~ s(Temp) >>> Resid. Df Resid. Dev Df Deviance F Pr(>F) >>> 1 3.5000e+01 3.279 >>> 2 3.5000e+01 3.279 5.5554e-10 2.353e-11 0.4521 6.18e-09 *** >>> >> >> >> Thanks in advance, >> >> >> Denis Chabot >> >> ______________________________________________ >> 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 >> > > ______________________________________________ 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