Statistical inferences on LME predictions Suppose that under a linear mixed-effects model using the R package nlme:
library(nlme)
fm <- lme(distance ~ age, random=~age, data = Orthodont)

I can assess the predicted difference of "distance" between the two ages (8.5 and 13.4) as follows:
predict(fm, data.frame(age=13.4), level = 0) - predict(fm, data.frame(age=8.5), level = 0)

[1] 3.234907
However, is there a way to estimate the standard error for the above predicted difference? 
 A: Using the predictSE.lme function from the AICcmodavg package will get you the predicted value and it's standard error. If you are comparing the two predicted values, couldn't you calculate the standard error of the difference between means as sqrt(se_1^2 + se_2^2) and derive your Confidence Intervals around the different from there?
library(nlme)
fm <- lme(distance ~ age, random=~age, data = Orthodont)

predict(fm, data.frame(age=13.4), level = 0) - predict(fm, data.frame(age=8.5), level = 0)


library(AICcmodavg)

mean_diff <- predictSE.lme(fm, data.frame(age=13.4), level = 0)$fit - predictSE.lme(fm, data.frame(age=8.5), level = 0)$fit
mean_diff

se_diff <- sqrt(predictSE.lme(fm, data.frame(age=13.4), level = 0)$se.fit^2 + predictSE.lme(fm, data.frame(age=8.5), level = 0)$se.fit^2)
se_diff


Low_CI95 <- mean_diff - 1.96*se_diff
High_CI95 <- mean_diff + 1.96*se_diff


list("Mean Difference" = mean_diff,
    "95% Confidence Interval" = c(Low_CI95, High_CI95))

$`Mean Difference`
[1] 3.234907

$`95% Confidence Interval`
[1] 1.952055 4.517760

