Equal standard errors for all levels of a categorical factor in lmer I have a question about the standard error of mixed model parameters estimated using the lmerTest package.
I have 12 sites with 6 treatments over each site. I measured a response variable (biomass_of_insects) (which has a Gaussian distribution). 
library (lmerTest)  
model <- lmer(biomass_of_insects ~ as.factor(treatments) + (1 | sites))

However, the model summary shows the same standard error for every treatment (see below: 114.065). Why is the standard error always the same? 
Fixed effects:        
                       Estimate    Std.err      df       t        p
(Intercept)             501.333     80.656  66.000   6.216 3.91e-08 ***
as.factor(treat)F       126.667    114.065  66.000   1.110    0.271 
as.factor(treat)I        -8.333    114.065  66.000  -0.073    0.942     
as.factor(treat)I+F1/3  -75.000    114.065  66.000  -0.658    0.513   
as.factor(treat)I+F2/3   18.333    114.065  66.000   0.161    0.873    
as.factor(treat)I+F3/3   15.917    114.065  66.000   0.140    0.889 

 A: The short answer is "because there's the same amount of information in the data about each treatment" -- your data are balanced.  I'll illustrate with the Product effect standard errors from the ham example included with the lmerTest package. Computing with(ham,table(Product)) shows the data are balanced with respect to Product.  The standard errors would differ if the data were unbalanced, as for example:
library("lmerTest")
## model of balanced data: summary(m) will give identical std errs
m <- lmer(Informed.liking ~ Gender+Information+Product +
   (1|Consumer), data=ham) 
## now randomly sample half the data set (very unlikely to produce a 
##  balanced data set)
set.seed(101); dd <- ham[sample(nrow(ham),size=nrow(ham)/2),]
with(dd,table(Product))   
## Product
##  1  2  3  4 
## 82 78 80 84 
summary(update(m,data=dd))
...
##              Estimate Std. Error t value
## Product2     -0.25309    0.31769  -0.797
## Product3      0.56563    0.31676   1.786
## Product4      0.31761    0.31035   1.023

The standard errors are still very similar (because the data set is only slightly unbalanced), but no longer identical.
