From: John Fox <jfox_at_mcmaster.ca>

Date: Wed 05 Oct 2005 - 23:45:03 EST

John Fox

Department of Sociology

McMaster University

Hamilton, Ontario

Canada L8S 4M4

905-525-9140x23604

http://socserv.mcmaster.ca/jfox

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 Thu Oct 06 00:07:40 2005

Date: Wed 05 Oct 2005 - 23:45:03 EST

John Fox

Department of Sociology

McMaster University

Hamilton, Ontario

Canada L8S 4M4

905-525-9140x23604

http://socserv.mcmaster.ca/jfox

> -----Original Message-----

*> From: r-help-bounces@stat.math.ethz.ch
**> [mailto:r-help-bounces@stat.math.ethz.ch] 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 Received on Thu Oct 06 00:07:40 2005

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