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

["Biedermann, Jürgen"]

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?

Greetings and thanks in advance
Jürgen