R version 4.4.0 beta (2024-04-14 r86421 ucrt) -- "Puppy Cup"
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> ## In both of these cases boundary fit (i.e. estimate of zero RE
> ## variance) is *incorrect*. (Nelder_Mead, restart_edge=FALSE) is the
> ## only case where we get stuck; either optimizer=bobyqa or
> ## restart_edge=TRUE (default) works
> if (.Platform$OS.type != "windows") {
+ 
+     library(lme4)
+     library(testthat)
+ 
+     if(!dev.interactive(orNone=TRUE)) pdf("boundary_plots.pdf")
+ 
+     ## Stephane Laurent:
+     dat <- read.csv(system.file("testdata","dat20101314.csv", package="lme4"))
+ 
+     fit   <- lmer(y ~ (1|Operator)+(1|Part)+(1|Part:Operator), data=dat,
+                   control= lmerControl(optimizer="Nelder_Mead"))
+     fit_b <- lmer(y ~ (1|Operator)+(1|Part)+(1|Part:Operator), data=dat,
+                   control= lmerControl(optimizer="bobyqa", restart_edge=FALSE))
+     fit_c <- lmer(y ~ (1|Operator)+(1|Part)+(1|Part:Operator), data=dat,
+                   control= lmerControl(optimizer="Nelder_Mead", restart_edge=FALSE,
+                                        check.conv.hess="ignore"))
+     ## final fit gives degenerate-Hessian warning
+     ## FIXME: use fit_c with expect_warning() as a check on convergence tests
+     ## tolerance=1e-5 seems OK in interactive use but not in R CMD check ... ??
+     stopifnot(all.equal(getME(fit,  "theta") -> th.f,
+                         getME(fit_b,"theta"), tolerance=5e-5),
+               all(th.f > 0))
+ 
+     ## Manuel Koller
+ 
+     source(system.file("testdata", "koller-data.R", package="lme4"))
+     ldata <- getData(13)
+     ## old (backward compatible/buggy)
+     fm4  <- lmer(y ~ (1|Var2), ldata, control=lmerControl(optimizer="Nelder_Mead",
+                                                           use.last.params=TRUE),
+                  start=list(theta=1))
+ 
+     fm4b <- lmer(y ~ (1|Var2), ldata,
+                  control = lmerControl(optimizer="Nelder_Mead", use.last.params=TRUE,
+                                        restart_edge = FALSE,
+                                        check.conv.hess="ignore", check.conv.grad="ignore"),
+                  start = list(theta=1))
+     ## FIXME: use as convergence test check
+     stopifnot(getME(fm4b,"theta") == 0)
+     fm4c <- lmer(y ~ (1|Var2), ldata, control=lmerControl(optimizer="bobyqa",
+                                                           use.last.params=TRUE),
+                  start=list(theta=1))
+     stopifnot(all.equal(getME(fm4, "theta") -> th4,
+                         getME(fm4c,"theta"), tolerance=1e-4),
+               th4 > 0)
+ 
+ 
+     ## new: doesn't get stuck at edge any more,  but gets stuck somewhere else ...
+     fm5 <- lmer(y ~ (1|Var2), ldata, control=lmerControl(optimizer="Nelder_Mead",
+                                                          check.conv.hess="ignore",
+                                                          check.conv.grad="ignore"),
+                 start=list(theta=1))
+     fm5b <- lmer(y ~ (1|Var2), ldata, control=lmerControl(optimizer="Nelder_Mead",
+                                                           restart_edge=FALSE,
+                                                           check.conv.hess="ignore",
+                                                           check.conv.grad="ignore"),
+                  start = list(theta = 1))
+     fm5c <- lmer(y ~ (1|Var2), ldata, control=lmerControl(optimizer="bobyqa"),
+                  start = list(theta = 1))
+     stopifnot(all.equal(unname(getME(fm5c,"theta")), 0.21067645, tolerance = 1e-7))
+ 					#	 0.21067644264 [64-bit, lynne]
+ 
+     if (require("optimx")) {
+     ## additional stuff for diagnosing Nelder-Mead problems.
+ 
+     fm5d <- update(fm5,control=lmerControl(optimizer="optimx",
+                                            optCtrl=list(method="L-BFGS-B")))
+ 
+     fm5e <- update(fm5, control=lmerControl(optimizer="nloptwrap"))
+ 
+     mList <- setNames(list(fm4,fm4b,fm4c,fm5,fm5b,fm5c,fm5d,fm5e),
+                       c("NM/uselast","NM/uselast/norestart","bobyqa/uselast",
+                         "NM","NM/norestart","bobyqa","LBFGSB","nloptr/bobyqa"))
+     pp <- profile(fm5c,which=1)
+     dd <- as.data.frame(pp)
+     par(las=1,bty="l")
+     v <- sapply(mList,
+                 function(x) sqrt(VarCorr(x)[[1]]))
+     plot(.zeta^2~.sig01, data=dd, type="b")
+     abline(v=v)
+ 
+     res <- cbind(VCorr  = sapply(mList, function(x) sqrt(VarCorr(x)[[1]])),
+                  theta  = sapply(mList, getME,"theta"),
+                  loglik = sapply(mList, logLik))
+     res
+     print(sessionInfo(), locale=FALSE)
+     }
+ 
+ ######################
+     library(lattice)
+     ## testing boundary and near-boundary cases
+ 
+     tmpf <- function(i,...) {
+         set.seed(i)
+         d <- data.frame(x=rnorm(60),f=factor(rep(1:6,each=10)))
+         d$y <- simulate(~x+(1|f),family=gaussian,newdata=d,
+                         newparams=list(theta=0.01,beta=c(1,1),sigma=5))[[1]]
+         lmer(y~x+(1|f),data=d,...)
+     }
+     sumf <- function(m) {
+         unlist(VarCorr(m))[1]
+     }
+     if (FALSE) {
+         ## figuring out which seeds will give boundary and
+         ## near-boundary solutions
+         mList <- lapply(1:201,tmpf) # [FIXME tons of messages "theta parameters vector not named"]
+         ss <- sapply(mList,sumf)+1e-50
+         par(las=1,bty="l")
+         hist(log(ss),col="gray",breaks=50)
+         ## values lying on boundary
+         which(log(ss)<(-40))   ## 5, 7-13, 15, 21, ...
+         ## values close to boundary (if check.edge not set)
+         which(log(ss)>(-40) & log(ss) <(-20))  ## 16, 44, 80, 86, 116, ...
+     }
+     ## diagnostic plot
+     tmpplot <- function(i, FUN=tmpf) {
+         dd <- FUN(i, devFunOnly=TRUE)
+         x <- 10^seq(-10,-6.5,length=201)
+         dvec <- sapply(x,dd)
+         op <- par(las=1,bty="l"); on.exit(par(op))
+         plot(x,dvec-min(dvec)+1e-16, log="xy", type="b")
+         r <- FUN(i)
+         abline(v = getME(r,"theta"), col=2)
+         invisible(r)
+     }
+ 
+     ## Case #1: boundary estimate with or without boundary.tol
+     m5  <- tmpf(5)
+     m5B <- tmpf(5,control=lmerControl(boundary.tol=0))
+     stopifnot(getME(m5, "theta")==0,
+               getME(m5B,"theta")==0)
+     p5 <- profile(m5)  ## bobyqa warnings but results look reasonable
+     xyplot(p5)
+     ## reveals slight glitch (bottom row of plots doesn't look right)
+     expect_warning(splom(p5),"unreliable for singular fits")
+     p5B <- profile(m5, signames=FALSE) # -> bobyqa convergence warning (code 3)
+     expect_warning(splom(p5B), "unreliable for singular fits")
+ 
+     if(lme4:::testLevel() >= 2) { ## avoid failure to warn
+         ## Case #2: near-boundary estimate, but boundary.tol can't fix it
+         m16 <- tmpplot(16)
+         ## sometimes[2014-11-11] fails (??) :
+         p16 <- profile(m16)  ## warning message*s* (non-monotonic profile and more)
+         plotOb <- xyplot(p16)
+         ## NB: It's the print()ing of 'plotOb' which warns ==> need to do this explicitly:
+         expect_warning(print(plotOb), ## warns about linear interpolation in profile for variable 1
+                        "using linear interpolation")
+         d16 <- as.data.frame(p16)
+         xyplot(.zeta ~ .focal|.par, data=d16, type=c("p","l"),
+                scales = list(x=list(relation="free")))
+         try(splom(p16))  ## breaks when calling predict(.)
+     }
+ 
+     ## bottom line:
+     ##  * xyplot.thpr could still be improved
+     ##  * most of the near-boundary cases are noisy and can't easily be
+     ##    fixed
+ 
+     tmpf2 <- function(i,...) {
+         set.seed(i)
+         d <- data.frame(x=rnorm(60),f=factor(rep(1:6,each=10)),
+                         w=rep(10,60))
+         d$y <- simulate(~x+(1|f),family=binomial,
+                         weights=d$w,newdata=d,
+                         newparams=list(theta=0.01,beta=c(1,1)))[[1]]
+         glmer(y~x+(1|f),data=d,family=binomial,weights=w,...)
+     }
+ 
+     if (FALSE) {
+         ## figuring out which seeds will give boundary and
+         ## near-boundary solutions
+         mList <- lapply(1:201,tmpf2)
+         ss <- sapply(mList,sumf)+1e-50
+         par(las=1,bty="l")
+         hist(log(ss),col="gray",breaks=50)
+         ## values lying on boundary
+         head(which(log(ss)<(-50)))   ## 1-5, 7 ...
+         ## values close to boundary (if check.edge not set)
+         which(log(ss)>(-50) & log(ss) <(-20))  ## 44, 46, 52, ...
+     }
+ 
+     ##  m1 <- tmpf2(1)
+ 
+     ## FIXME: doesn't work if we generate m1 via tmpf2(1) --
+     ## some environment lookup problem ...
+ 
+     set.seed(1)
+     d <- data.frame(x=rnorm(60),f=factor(rep(1:6,each=10)),
+                     w=rep(10,60))
+     d$y <- simulate(~x+(1|f),family=binomial,
+                     weights=d$w,newdata=d,
+                     newparams=list(theta=0.01,beta=c(1,1)))[[1]]
+     m1 <- glmer(y~x+(1|f),data=d,family=binomial,weights=w)
+ 
+     p1 <- profile(m1)
+     xyplot(p1)
+     expect_warning(splom(p1),"splom is unreliable")
+ 
+ } ## skip on windows (for speed)
> 
> proc.time()
   user  system elapsed 
   0.18    0.04    0.23