Just for fun, I decided to compare the estimates from lmer and INLA for the variance components of an LMM (this isn’t really something that you would ordinarily do – comparing frequentist and bayesian approaches). The codes are below. A couple of plots are drawn, which show the distribution of the hyperparameters (in this case variances) from INLA, which are difficult to get from the frequentist framework (there’s a link to a presentation by Douglas Bates in the code, detailing why you might not want to do it [distribution is not symmetrical], and how you could do it… but it’s a lot of work).

Note that we’re comparing the precision (tau) rather than the variance or SD… SD = 1/sqrt(tau)

As you’d hope, the results come pretty close to each other and the truth:

cbind(truth = c(tau, tau.ri), lmer = 1/c(attr(vc, "sc")^2, unlist(vc)), inla = imod$summary.hyperpar$`0.5quant`)
      truth      lmer      inla
       3.00 2.9552444 2.9556383
group  0.25 0.2883351 0.2919622

Code on Github…