[R] How to test omitted level from a multiple level factor against overall mean in regression models?

["Biedermann, Jürgen"]

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 [ggrothendieck at gmail.com]
Gesendet: Sonntag, 25. März 2012 14:11
An: Biedermann, Jürgen
Cc: r-help at 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.Biedermann at 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

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