The test you are requesting is ***MEANINGLESS***. The ``effect value'' of a single level is ill-defined (or in the more usual parlance, "not estimable"). The dummy.coef() procedure suggested by Gabor gives you point estimates *subject to the constraints* imposed by the contrasts used. The choice of contrasts is arbitrary, essentially a matter of aesthetics/taste/convenience. The values returned by dummy.coef() have, in and
of themselves, no meaning at all.
You can meaningfully estimate, and test for the "significance" of, *differences* between the "effect values" of factor levels. For the individual levels, no can do.
E.g. Y = mu + alpha_i + E when the observation is at level i of the factor (and "E" means "random error". In this setting mu = 0, alpha_1 = 1, alpha_2 = 2 and alpha_3
= 3 is ***EXACTLY THE SAME MODEL*** as mu = 1, alpha_1 = 0, alpha_2 = 1 and
alpha_3 = 2.
It makes no sense to ask (or to test) whether alpha_1 differs from 0.
cheers,
Rolf Turner
On 26/03/12 02:08, "Biedermann, Jürgen" wrote:
Hi Gabor, Thanks a lot for the answer. However, I'm not so much focusing on the pure effect value of the omitted factor level, but more on the statistical test if it differs significantly from 0. Do you know a way for this purpose too? Greetings Jürgen ________________________________________ Von: Gabor Grothendieck [ggrothendi...@gmail.com] Gesendet: Sonntag, 25. März 2012 14:11 An: Biedermann, Jürgen Cc: r-help@R-project.org Betreff: Re: [R] How to test omitted level from a multiple level factor against overall mean in regression models? 2012/3/25 "Biedermann, Jürgen"<juergen.biederm...@charite.de>:Hi there, I have a linear model with one factor having three levels. I want to check if the different levels significantly differ from the overall mean (using contr.sum). However one level (the last) is omitted in the standard procedure. To illustrate this: x<- as.factor(c(1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3)) y<- c(1.1,1.15,1.2,1.1,1.1,1.1,1.2,1.2,1.2,2.1,2.2,2.3,2.4,2.5,2.6,2.7,2.8,2.9,3,3.1) test<- data.frame(x,y) reg1<- lm(y~C(x,contr.sum),data=test) summary(reg1) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.63333 0.06577 24.834 8.48e-15 *** C(x, contr.sum)1 -0.48333 0.10792 -4.479 0.00033 *** C(x, contr.sum)2 -0.48333 0.08936 -5.409 4.70e-05 *** Is it possible to get the effect for the third level (against the overall mean) in the table too. I figured out: reg2<- lm(y~C(relevel(x,3),contr.sum),data=test) summary(reg2) C(relevel(x, 3), contr.sum)1 0.96667 0.07951 12.158 8.24e-10 *** C(relevel(x, 3), contr.sum)2 -0.48333 0.10792 -4.479 0.00033 *** The first row now test the third level against the overall mean, but I find this approach not so convenient. Moreover, I wonder if it is meaningful at all regarding the cumulation of alpha error. Would a Bonferroni correction be sensible?Try this:options(contrasts = c("contr.sum", "contr.poly")) reg1<- lm(y~x,data=test) dummy.coef(reg1)Full coefficients are (Intercept): 1.633333 x: 1 2 3 -0.4833333 -0.4833333 0.9666667 -- Statistics& Software Consulting GKX Group, GKX Associates Inc. tel: 1-877-GKX-GROUP email: ggrothendieck at gmail.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.
______________________________________________ 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.
