R Under development (unstable) (2023-07-03 r84633 ucrt) -- "Unsuffered Consequences"
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> library(lme4)
Loading required package: Matrix
> n <- nrow(sleepstudy)
> op <- options(warn = 1, # show as they happen ("false" convergence warnings)
+               useFancyQuotes = FALSE)
> 
> if (.Platform$OS.type != "windows") {
+ ##' remove all attributes but names
+ dropA <- function(x) `attributes<-`(x, list(names = names(x)))
+ ##' transform result of "numeric" all.equal.list() to a named vector
+ all.eqL <- function(x1, x2, ...) {
+     r <- sub("^Component ", '', all.equal(x1, x2, tolerance = 0, ...))
+     r <- strsplit(sub(": Mean relative difference:", "&&", r),
+                   split="&&", fixed=TRUE)
+     setNames(as.numeric(vapply(r, `[`, "1.234", 2L)),
+              ## drop surrounding "..."
+              nm = sub('"$', '', substring(vapply(r, `[`, "nam",   1L), first=2)))
+ }
+ seedF <- function(s) {
+     if(s %in% c(6, 39, 52, 57, 63, 74, 76, 86))
+         switch(as.character(s)
+                , "52"=, "63"=, "74" = 2
+                , "6"=, "39" = 3
+                , "86" =  8 # needs  4 on Lnx-64b
+                , "76" = 70 # needs 42 on Lnx-64b
+                , "57" = 90 # needs 52 on Lnx-64b
+                )
+     else if(s %in% c(1, 12, 15, 34, 36, 41, 42, 43, 49, 55, 59, 67, 80, 85)) ## seeds 41,59, .. 15
+         1.0
+     else ## seeds 22, 20, and better
+         0.25
+ }
+ ## be fast, running only 10 seeds by default:
+ sMax <- if(lme4:::testLevel() > 1) 99L else 9L
+ mySeeds <- 0L:sMax
+ 
+ lapply(setNames(,mySeeds), function(seed) {
+     cat("\n------ random seed =", seed, "---------\n")
+     set.seed(seed)
+     v <- rpois(n,1) + 1
+     w <- 1/v
+     cat("weights w:\n")
+     fm1    <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy, REML=FALSE, weights = w); cat("..2:\n")
+     fm2    <- lmer(Reaction ~ Days + (1    | Subject), sleepstudy, REML=FALSE, weights = w)
+     cat("weights w*10:\n")
+     fm1.10 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy, REML=FALSE, weights = w*10);cat("..2:\n")
+     fm2.10 <- lmer(Reaction ~ Days + (1    | Subject), sleepstudy, REML=FALSE, weights = w*10)
+     ##
+     ano12... <- dropA(anova(fm1,    fm2   ))
+     ano12.10 <- dropA(anova(fm1.10, fm2.10))
+     print(aEQ <- all.eqL(ano12..., ano12.10)) # showing differences
+     if(!exists("notChisq"))
+ 	notChisq <<-
+ 	    local({ n <- names(ano12...)
+ 		grep("Chisq", n, value=TRUE, fixed=TRUE, invert=TRUE) })
+     stopifnot(
+         all.equal(ano12...$Chisq,
+                   ano12.10$Chisq, tol = 1e-6 * seedF(seed))
+        ,
+         all.equal(ano12...[notChisq],
+                   ano12.10[notChisq], tol= 1.5e-8 * seedF(seed))
+     )
+     aEQ
+ }) -> rallEQ
+ 
+ cat("=====================================\n")
+ 
+ rallEQ <- t(simplify2array(rallEQ))
+ notChisq <- intersect(notChisq, colnames(rallEQ))
+ ## sort according to "severity":
+ srallEQ <- rallEQ[with(as.data.frame(rallEQ), order(AIC, Chisq)), ]
+ round(log10(srallEQ), 2)
+ saveRDS(srallEQ, "priorWeightsMod_relerr.rds")
+ 
+ if(!dev.interactive(orNone=TRUE)) pdf("priorWeightsMod_relerr.pdf")
+ 
+ matplot(mySeeds, log10(srallEQ), type="l", xlab=NA) ; grid()
+ legend("topleft", ncol=3, bty="n",
+        paste(1:6, colnames(srallEQ), sep = ": "), col=1:6, lty=1:6)
+ tolD <- sqrt(.Machine$double.eps) # sqrt(eps_C)
+ abline(h = log10(tolD), col = "forest green", lty=3)
+ axis(4, at=log10(tolD), label=quote(sqrt(epsilon[c])), las=1)
+ LRG <- which(srallEQ[,"AIC"] > tolD)
+ if (length(LRG)>0) {
+     text(LRG, log10(srallEQ[LRG, "AIC"]), names(LRG), cex = .8)
+ }
+ 
+ ## how close are we ..
+ str(tF <- sapply(mySeeds, seedF))
+ round(sort(      rallEQ[, "Chisq"] / (tF * 1e-6  ),          decreasing=TRUE), 1)
+ round(sort(apply(rallEQ[,notChisq] / (tF * 1.5e-8), 1, max), decreasing=TRUE), 1)
+ } ## skip on windows (for speed)
> options(op)
> 
> proc.time()
   user  system elapsed 
   1.06    0.17    1.23