[R-sig-ME] comparing posterior means
Jake Westfall
jake987722 at hotmail.com
Wed Oct 15 22:06:46 CEST 2014
Hi Ben,
It seems to me that if you are interested in the differences between particular countries then you should strongly reconsider whether it is really appropriate to be treating countries as random effects in the first place. And this is obviously a much easier kind of question to answer if countries are fixed. After reconsidering this you might still maintain that treating them as random is best, which is fine, I just want to make sure that you have at least considered the fixed possibility.
Jake
> From: HDoran at air.org
> To: b.pelzer at maw.ru.nl; r-sig-mixed-models at r-project.org
> Date: Wed, 15 Oct 2014 14:30:02 +0000
> Subject: Re: [R-sig-ME] comparing posterior means
>
> Ben
>
> Yes, you can do this comparison of the conditional means using the variance of the linear combination AND there is in fact a covariance term between them. I do not believe that covariance term between BLUPs is available in lmer (I wrote my own mixed model function that does spit this out, however).
>
> Just to be didactic for a moment. Take a look at Henderson's equation(say at the link below)
>
> http://en.wikipedia.org/wiki/Mixed_model
>
> The covariance term between the blups that you would need comes from the lower right block of the leftmost matrix at the final solution. Lmer is not parameterized this way, so the comparison is not intended to show how that term would be extracted from lmer. Only to show that is does exist in the likelihood and can (conceivably) be extracted or computed from the terms given by lmer.
>
>
>
> -----Original Message-----
> From: r-sig-mixed-models-bounces at r-project.org [mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of Ben Pelzer
> Sent: Wednesday, October 15, 2014 8:56 AM
> To: r-sig-mixed-models at r-project.org
> Subject: [R-sig-ME] comparing posterior means
>
> 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 residual 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,
>
> Ben.
>
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