BLUB´s (random effect predictions/random coefficients) seems to be calculated by scaling the centered Means with the Variance Component divided by Variance of Means. However, this causes BLUB´s to have a lower standard deviation than the square root of the variance component. If they were scaled by the square root of the Variance Component divided by Variance of Means, the standard deviation of the BLUB´s would be equal to the square root of the variance component. BLUB´s are shown on a profiler in Mixed Model, so I assume they should be unbiased estimates of the means for each level of the random factor? See attached example.
