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> ## compare range, average, etc. of simulations to
> ## conditional and unconditional prediction
> library(lme4)
Loading required package: Matrix
> do.plot <- FALSE
> 
> if (.Platform$OS.type != "windows") {
+ ## use old (<=3.5.2) sample() algorithm if necessary
+ if ("sample.kind" %in% names(formals(RNGkind))) {
+     suppressWarnings(RNGkind("Mersenne-Twister", "Inversion", "Rounding"))
+ }
+ 
+ fm1 <- lmer(Reaction~Days+(1|Subject),sleepstudy)
+ set.seed(101)
+ pp <- predict(fm1)
+ rr <- range(usim2 <- simulate(fm1,1,use.u=TRUE)[[1]])
+ stopifnot(all.equal(rr,c(159.3896,439.1616),tolerance=1e-6))
+ if (do.plot) {
+     plot(pp,ylim=rr)
+     lines(sleepstudy$Reaction)
+     points(simulate(fm1,1)[[1]],col=4)
+     points(usim2,col=2)
+ }
+ 
+ set.seed(101)
+ 
+ ## conditional prediction
+ ss <- simulate(fm1,1000,use.u=TRUE)
+ ss_sum <- t(apply(ss,1,quantile,c(0.025,0.5,0.975)))
+ plot(pp)
+ matlines(ss_sum,col=c(1,2,1),lty=c(2,1,2))
+ stopifnot(all.equal(ss_sum[,2],pp,tolerance=5e-3))
+ 
+ ## population-level prediction
+ pp2 <- predict(fm1,ReForm=NA)
+ ss2 <- simulate(fm1,1000,use.u=FALSE)
+ ss_sum2 <- t(apply(ss2,1,quantile,c(0.025,0.5,0.975)))
+ 
+ if (do.plot) {
+     plot(pp2,ylim=c(200,400))
+     matlines(ss_sum2,col=c(1,2,1),lty=c(2,1,2))
+ }
+ 
+ stopifnot(all.equal(ss_sum2[,2],pp2,tolerance=8e-3))
+ 
+ ## predict(...,newdata=...) on models with derived variables in the random effects
+ ## e.g. (f:g, f/g)
+ set.seed(101)
+ d <- expand.grid(f=factor(letters[1:10]),g=factor(letters[1:10]),
+                  rep=1:10)
+ d$y <- rnorm(nrow(d))
+ m1 <- lmer(y~(1|f:g),d)
+ p1A <- predict(m1)
+ p1B <- predict(m1,newdata=d)
+ stopifnot(all.equal(p1A,p1B))
+ m2 <- lmer(y~(1|f/g),d)
+ p2A <- predict(m2)
+ p2B <- predict(m2,newdata=d)
+ stopifnot(all.equal(p2A,p2B))
+ 
+ ## with numeric grouping variables
+ dn <- transform(d,f=as.numeric(f),g=as.numeric(g))
+ m1N <- update(m1,data=dn)
+ p1NA <- predict(m1N)
+ p1NB <- predict(m1N,newdata=dn)
+ stopifnot(all.equal(p1NA,p1NB))
+ 
+ ## simulate with modified parameters
+ set.seed(1)
+ s1 <- simulate(fm1)
+ set.seed(1)
+ s2 <- simulate(fm1,newdata=model.frame(fm1),
+                newparams=getME(fm1,c("theta","beta","sigma")))
+ all.equal(s1,s2)
+ 
+ fm0 <- update(fm1,.~.-Days)
+ ##
+ ## sim() -> simulate() -> refit() -> deviance
+ ##
+ 
+ ## predictions and simulations with offsets
+ 
+ set.seed(101)
+ d <- data.frame(y=rpois(100,5),x=rlnorm(100,1,1),
+                 f=factor(sample(10,size=100,replace=TRUE)))
+ gm1 <- glmer(y~offset(log(x))+(1|f),data=d,
+              family=poisson)
+ s1 <- simulate(gm1)
+ } ## skip on windows (for speed)
> 
> proc.time()
   user  system elapsed 
   1.56    0.20    1.73