R Under development (unstable) (2023-07-03 r84633 ucrt) -- "Unsuffered Consequences"
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> if (.Platform$OS.type != "windows") {
+     ## test of false zero problem reported by Vince Dorie
+     ## (no longer occurs with current development lme4)
+     ## https://github.com/lme4/lme4/issues/17
+     library(lme4)
+ 
+     sigma.eps <- 2
+     sigma.the <- 0.75
+     mu <- 2
+ 
+     n <- 5
+     J <- 10
+     g <- gl(J, n)
+ 
+     set.seed(1)
+ 
+     theta <- rnorm(J, 0, sigma.eps * sigma.the)
+     y <- rnorm(n * J, mu + theta[g], sigma.eps)
+     lmerFit <- lmer(y ~ 1 + (1 | g), REML = FALSE, verbose=TRUE)
+ 
+     y.bar <- mean(y)
+     y.bar.j <- sapply(1:J, function(j) mean(y[g == j]))
+     S.w <- sum((y - y.bar.j[g])^2)
+     S.b <- n * sum((y.bar.j - y.bar)^2)
+     R <- S.b / S.w
+ 
+     sigma.the.hat <- sqrt(max((n - 1) * R / n - 1 / n, 0))
+     stopifnot(all.equal(sigma.the.hat,lme4Sigma <- unname(getME(lmerFit,"theta")),
+                         tolerance=2e-5))
+ } ## skip on windows (for speed)
> 
> proc.time()
   user  system elapsed 
   0.09    0.06    0.14