The `concentration` parameter in `decov` has no effect.

Hello,

Here is a model with two between variances:

library(rstanarm)
rstanarm <- stan_lmer(
  y ~  0 + Part + (1|Operator) + (1|Operator:Part), data = dat,
  prior = normal(0, 100),
  prior_aux = cauchy(0, 5),
  prior_covariance = decov(concentration = 1000000, shape = 1, scale = 1/1),
  iter = 10000
)
posterior_interval(rstanarm, prob = 95/100)

From my understanding, if the concentration parameter is high (here 1e6), the two between variances should be equal. But this is not the case:

                                                      2.5%      97.5%
PartA1                                        7.6725149693 10.9984804
PartA2                                       17.7830860979 21.1723343
...
sigma                                         1.5266337590  2.3625997
Sigma[Operator:Part:(Intercept),(Intercept)]  0.0004819209  3.6359430
Sigma[Operator:(Intercept),(Intercept)]       0.0251682030 10.6149320

And I don't see any significant difference when I set it to 1.

To reproduce the data:

SimAV2mixed <- function(I, J, Kij, mu=0, alphai, sigmaO=1,
                        sigmaPO=1, sigmaE=1, factor.names=c("Part","Operator"),
                        resp.name="y", keep.intermediate=FALSE){
  Operator <- rep(1:J, each=I)
  Oj <- rep(rnorm(J, 0, sigmaO), each=I)
  Part <- rep(1:I, times=J)
  Pi <- rep(alphai, times=J)
  POij <- rnorm(I*J, 0, sigmaPO)
  simdata0 <- data.frame(Part, Operator, Pi, Oj, POij)
  simdata0$Operator <- factor(simdata0$Operator)
  levels(simdata0$Operator) <- 
    sprintf(paste0("%0", floor(log10(J))+1, "d"), 1:J)
  simdata0$Part <- factor(simdata0$Part)
  levels(simdata0$Part) <- sprintf(paste0("%0", floor(log10(I))+1, "d"), 1:I)
  simdata <- 
    as.data.frame(
      sapply(simdata0, function(v) rep(v, times=Kij), simplify=FALSE))
  Eijk <- rnorm(sum(Kij), 0, sigmaE)
  simdata <- cbind(simdata, Eijk)
  simdata[[resp.name]] <- mu + with(simdata, Oj+Pi+POij+Eijk)
  levels(simdata[,1]) <- paste0("A", levels(simdata[,1]))
  levels(simdata[,2]) <- paste0("B", levels(simdata[,2]))
  names(simdata)[1:2] <- factor.names
  if(!keep.intermediate) simdata <- simdata[,c(factor.names,resp.name)]
  simdata
}

set.seed(666)  
I = 2; J = 6; Kij = rpois(I*J, 1) + 3
alphai <- c(10, 20)
sigmaO <- 1
sigmaPO <- 0.5
sigmaE <- 2
dat <- SimAV2mixed(I, J, Kij, mu = 0, alphai = alphai, 
                   sigmaO = sigmaO, sigmaPO = sigmaPO, sigmaE = sigmaE)

Start with the supplied stan_lmer and decov reproduction, using the provided SimAV2mixed data-generating function and posterior_interval output. Trace how changing concentration from 1 to 1e6 is represented in the covariance prior, then verify that the resulting between-group variance behavior matches the documented expectation.