Gavin, Thank you for your clear explanation. I'm just learning R, hence my not knowing how to dummy code a variable using R. Your example was very useful!
Thank you again. Lidia ---------------------------------------- > Subject: Re: [R] Interpretation of gam intercept parameter > From: gavin.simp...@ucl.ac.uk > To: lidiadob...@hotmail.com > CC: r-help@r-project.org > Date: Wed, 30 Jun 2010 08:31:45 +0100 > > On Tue, 2010-06-29 at 21:27 -0500, Lidia Dobria wrote: >> Dear All: >> >> I apologize for asking such an elementary question, but I could not >> find an adequate response on line. I am hoping to receive some help >> with the interpretation of the Intercept coefficient in the gam model >> below. >> >> I1 through I3 are dummy coded "Item difficulty" parameters in a data >> set that includes 4 items. If the Intercept is the value of Y when all >> other terms are 0, am I correct in assuming that it also equals the >> difficulty of item 4 (dummy coded 0 0 0 )? > > If I understand you correctly (?) you have a single variable 'ID' (Item > Difficulty) taking three levels 1,2,3. If so, you should avoid making > your dummy variables by hand and let R's formula handling sugar take > care of this for you. > > fac <- factor(sample(rep(letters[1:3], each = 4))) > resp <- rnorm(12) > num <- rnorm(12) > model.matrix(resp ~ fac + num) > > (Intercept) facb facc num > 1 1 0 1 1.22373197 > 2 1 0 0 -0.23893032 > 3 1 1 0 -0.03588385 > 4 1 1 0 0.39657910 > 5 1 0 1 0.14727398 > 6 1 1 0 0.59727570 > 7 1 0 1 -0.24968044 > 8 1 0 0 0.01444002 > 9 1 0 1 0.45514437 > 10 1 1 0 -0.74748326 > 11 1 0 0 0.89873549 > 12 1 0 0 1.37584734 > attr(,"assign") > [1] 0 1 1 2 > attr(,"contrasts") > attr(,"contrasts")$fac > [1] "contr.treatment" > > With treatment contrasts the intercept is the mean for the reference > level (which is the first entry in levels(fac) ) and the facb and facc > entries above code for the difference in the mean response of the b and > c groups from the reference level mean (group a). To parametrise on the > group means, suppress the intercept > > model.matrix(resp ~ 0 + fac + num) ## or > model.matrix(resp ~ fac + num - 1) > > This all happens within the model fitting code, so I could run gam as: > > require(mgcv) > ## Probably good idea to have you data in a data frame > dat <- data.frame(fac, resp, num) > rm(resp, num, fac) > mod <- gam(resp ~ fac + s(num), data = dat) > summary(mod) > anova(mod) > > Compare the summary() and anova() output; in the former the data is at > the level of each coefficient (the treatment contrast info I mention > above), whilst in anova() the single term for fac combines this > information into a single value for the entire term 'fac'. > > If you want to alter the contrasts, look at ?contrasts > > Does it help if you recode your model using R's tools? > > G > >> >> Thank you for your help. >> Lidia >> >> >> Family: gaussian >> Link function: identity >> >> Formula: >> Score ~ I1 + I2 + I3 + s(TimeI1, bs = "cr", k = 7) + >> s(TimeI2, bs = "cr", k = 7) + s(TimeI3, bs = "cr", k = 7) >> >> Parametric coefficients: >> Estimate Std. Error t value Pr(>|t|) >> (Intercept) 4.70968 0.09547 49.330 < 2e-16 *** >> I1 -0.22188 0.21767 -1.019 0.308157 >> I2 0.51236 0.16592 3.088 0.002042 ** >> I3 -0.60697 0.18258 -3.324 0.000902 *** >> --- >> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 >> >> Approximate significance of smooth terms: >> edf Ref.df F p-value >> s(TimeI1) 3.820 3.820 4.587 0.001331 ** >> s(TimeI2) 2.491 2.491 6.271 0.000784 *** >> s(TimeI3) 3.481 3.481 8.997 1.54e-06 *** >> --- >> >> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 >> R-sq.(adj) = 0.057 Scale est. = 2.131 n = 2079 >> ______________________________________________ >> 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. > > -- > %~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~% > Dr. Gavin Simpson [t] +44 (0)20 7679 0522 > ECRC, UCL Geography, [f] +44 (0)20 7679 0565 > Pearson Building, [e] gavin.simpsonATNOSPAMucl.ac.uk > Gower Street, London [w] http://www.ucl.ac.uk/~ucfagls/ > UK. WC1E 6BT. [w] http://www.freshwaters.org.uk > %~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~% > ______________________________________________ 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.
