[R] SE for all fixed factor effect in GLMM

[Marc Girondot]

Dear members,

Let do a example of simple GLMM with x and G as fixed factors and R as 
random factor:

(note that question is the same with GLM or even LM):

x <- rnorm(100)
y <- rnorm(100)
G <- as.factor(sample(c("A", "B", "C", "D"), 100, replace = TRUE))
R <- as.factor(rep(1:25, 4))

library(lme4)

m <- lmer(y ~ x + G + (1 | R))
summary(m)$coefficients

I get the fixed effect fit and their SE

 > summary(m)$coefficients
                Estimate Std. Error    t value
(Intercept)  0.07264454  0.1952380  0.3720820
x           -0.02519892  0.1238621 -0.2034433
GB           0.10969225  0.3118371  0.3517614
GC          -0.09771555  0.2705523 -0.3611706
GD          -0.12944760  0.2740012 -0.4724344

The estimate for GA is not shown as it is fixed to 0. Normal, it is the 
reference level.

But is there a way to get SE for GA of is-it non-sense question because 
GA is fixed to 0 ?

______________

I propose here a solution but I don't know if it is correct. It is based 
on reordering levels and averaging se for all reordering:

G <- relevel(G, "A")
m <- lmer(y ~ x + G + (1 | R))
sA <- summary(m)$coefficients

G <- relevel(G, "B")
m <- lmer(y ~ x + G + (1 | R))
sB <- summary(m)$coefficients

G <- relevel(G, "C")
m <- lmer(y ~ x + G + (1 | R))
sC <- summary(m)$coefficients

G <- relevel(G, "D")
m <- lmer(y ~ x + G + (1 | R))
sD <- summary(m)$coefficients

seA <- mean(sB["GA", "Std. Error"], sC["GA", "Std. Error"], sD["GA", 
"Std. Error"])
seB <- mean(sA["GB", "Std. Error"], sC["GB", "Std. Error"], sD["GB", 
"Std. Error"])
seC <- mean(sA["GC", "Std. Error"], sB["GC", "Std. Error"], sD["GC", 
"Std. Error"])
seD <- mean(sA["GD", "Std. Error"], sB["GD", "Std. Error"], sC["GD", 
"Std. Error"])

seA; seB; seC; seD


Thanks,

Marc