lmer linear contrasts : Kenward Rogers or Satterthwaite DF and SE - r

Question

In R, I am searching for a way to estimate confidence intervals for linear contrasts for lmer models that use either kenward-rogers or satterthwaite degrees of freedom and SE.
For example, I can compute a CI for a fixed effect parameter in a mixed model like SAS with R, using the t-value (with df from KR) and SE.
mod<-lmerTest::lmer(y~time1+treatment+time1:treatment+(1|PersonID),data=data)
lmerTest::summary(mod,ddf = "Kenward-Roger")
This output:
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 49.0768 1.0435 56.4700 47.029 < 2e-16 ***
time1 5.8224 0.5963 48.0000 9.764 5.51e-13 ***
treatment 1.6819 1.4758 56.4700 1.140 0.2592
time1:treatment 2.0425 0.8433 48.0000 2.422 0.0193 *
Allows a CI for time1 like:
5.8224+abs(qt(0.05/2, 48))*0.5963 #7.021342
5.8224-abs(qt(0.05/2, 48))*0.5963 #4.623458
I would like to do this same thing for a linear contrast of the fixed coefficients. This is the p-value but there is no SE output.
pbkrtest::KRmodcomp(mod,matrix(c(0,0,1,0),nrow = 1))
stat ndf ddf F.scaling p.value
Ftest 1.2989 1.0000 56.4670 1 0.2592
Is there anyway to get a SE or a CI from lmer linear contrasts that uses this type of df?

Answer 1

For this, you have at least two options: using the lsmeans package, or doing it manually (using functions vcovAdj.lmerMod and pbkrtest::get_Lb_ddf). Personally, I go with the later if the contrast to be tested is not very "simple", because I find the syntax in lsmeans a bit complicated.
To exemplify, take the following model:
library(pbkrtest)
library(lme4)
library(nlme) # for the 'Orthodont' data
# 'age' is a numeric variable, while 'Sex' and 'Subject' are factors
model <- lmer(distance ~ age : Sex + (1 | Subject), data = Orthodont)
Linear mixed model fit by REML ['lmerMod']
Formula: distance ~ age:Sex + (1 | Subject)
…
Fixed Effects:
(Intercept) age:SexMale age:SexFemale
16.7611 0.7555 0.5215
from which we would like to obtain stats on the difference between the coefficients for age in males and females (i.e., age:SexMale - age:SexFemale).
Using lsmeans:
library(lsmeans)
# Evaluate the contrast at a value of 'age' set to 1,
# so that the resulting value is equal to the regression coefficient
lsm = lsmeans(model, pairwise ~ age : Sex, at = list(age = 1))$contrast
produces:
contrast estimate SE df t.ratio p.value
1,Male - 1,Female 0.2340135 0.06113276 42.64 3.828 0.0004
Alternatively, doing the calculation manually:
# Specify the contrasts: age:SexMale - age:SexFemale
# Must have the same order as the fixed effects in the model
K = c("(Intercept)" = 0, "age:SexMale" = 1, "age:SexFemale" = -1)
# Retrieve the adjusted variance-covariance matrix, to calculate the SE
V = pbkrtest::vcovAdj.lmerMod(model, 0)
# Point estimate, SE and df
point_est = sum(K * fixef(model))
SE = sqrt(sum(K * (V %*% K)))
df = pbkrtest::get_Lb_ddf(model, K)
alpha = 0.05 # significance level
# Calculate confidence interval for the difference between the 'age' coefficients for males and females
Delta_age_CI = point_est + SE * qt(c(0.5 * alpha, 1 - 0.5 * alpha), df)
will result in a point estimate equal to 0.2340135, SE 0.06113276, df 42.63844, and confidence interval [0.1106973, 0.3573297]