Extract prediction band from lme fit

Warning: Read this thread on r-sig-mixed models before doing this. Be very careful when you interpret the resulting prediction band.

From r-sig-mixed models FAQ adjusted to your example:

set.seed(42)x <- rep(0:100,10)y <- 15 + 2*rnorm(1010,10,4)*x + rnorm(1010,20,100)id<-rep(1:10,each=101)dtfr <- data.frame(x=x ,y=y, id=id)library(nlme)model.mx <- lme(y~x,random=~1+x|id,data=dtfr)#create data.frame with new values for predictors#more than one predictor is possiblenew.dat <- data.frame(x=0:100)#predict responsenew.dat$pred <- predict(model.mx, newdata=new.dat,level=0)#create design matrixDesignmat <- model.matrix(eval(eval(model.mx$call$fixed)[-2]), new.dat[-ncol(new.dat)])#compute standard error for predictionspredvar <- diag(Designmat %*% model.mx$varFix %*% t(Designmat))new.dat$SE <- sqrt(predvar) new.dat$SE2 <- sqrt(predvar+model.mx$sigma^2)library(ggplot2) p1 <- ggplot(new.dat,aes(x=x,y=pred)) + geom_line() +geom_ribbon(aes(ymin=pred-2*SE2,ymax=pred+2*SE2),alpha=0.2,fill="red") +geom_ribbon(aes(ymin=pred-2*SE,ymax=pred+2*SE),alpha=0.2,fill="blue") +geom_point(data=dtfr,aes(x=x,y=y)) +scale_y_continuous("y")p1

Sorry for coming back to such an old topic, but this might address a comment here:

it would be nice if some package could provide this functionality

This functionality is included in the ggeffects-package, when you use type = "re" (which will then include the random effect variances, not only residual variances, which is - however - the same in this particular example).

library(nlme)library(ggeffects)x  <- rep(seq(0, 100, by = 1), 10)y  <- 15 + 2 * rnorm(1010, 10, 4) * x + rnorm(1010, 20, 100)id <- NULLfor (i in 1:10) {  id <- c(id, rep(i, 101))}dtfr <- data.frame(x = x, y = y, id = id)m <- lme(y ~ x,         random =  ~ 1 + x | id,         data = dtfr,         na.action = na.omit)ggpredict(m, "x") %>% plot(rawdata = T, dot.alpha = 0.2)

ggpredict(m, "x", type = "re") %>% plot(rawdata = T, dot.alpha = 0.2)

^{Created on 2019-06-18 by the reprex package (v0.3.0)}