[R-sig-ME] comparing posterior means

Ben Pelzer b.pelzer at maw.ru.nl
Wed Oct 15 14:55:33 CEST 2014

Dear list,

Suppose we have the following two-level null-model, for data from 
respondents (lowest level 1) living in countries (highest level 2):

Y(ij) = b0j + eij = (b0 + u0j)  + eij

b0j is the country-mean for country j
b0 is the "grand mean"
u0j is the deviation from the grand mean for country j, or the level-2 
eij is the level-1 residual

The model is estimated by :  lmer(Y ~ 1+(1|country))

My question is about comparing two particular posterior country-means. 
As for as I know, for a given country j, the posterior mean is equal to 
bb0 + uu0j, where bb0 is the estimate of b0 and uu0j is the posterior 
residual estimate of u0j.

Two compare two particular posterior country means and test whether they 
differ significantly, would it be necessary to know the variance of 
bb0+uu0j for each of the two countries, or would it be sufficient to 
only know the variance of uu0j?

The latter variance (of uu0j) can be extracted using

rr <- ranef(modela, condVar=TRUE)
attr(rr[[1]], "postVar")

However, the variance of bb0+uu0j also depends on the variance of bb0 
and the covariance of bb0 and uu0j (if this covariance is not equal to 
zero, of course, which I don't know...).

On the other hand, the difference between two posterior country means 
for country A and B say, would
equal bb0 + u0A -(bb0 + u0B) = u0A - u0B meaning that I wouldn't need to 
worry about the variance of bb0.

So my main question is about comparing and testing the difference 
between two posterior country means. Thanks for any help,


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