var(ranef(Random Effect)) not the same as the variance component

Simon



Here is an example to show what my notation implies with respect to your
question:



fm1 <- lmer(Reaction ~ 1 + (1|Subject), sleepstudy)



sqrt(var(ranef(fm1)$Subject) + mean(sapply(attr(ranef(fm1,
condVar=TRUE)[[1]], "postVar"),function(x) x)))



*From:* Simon Harmel <sim.harmel at gmail.com>
*Sent:* Wednesday, September 9, 2020 11:53 AM
*To:* D. Rizopoulos <d.rizopoulos at erasmusmc.nl>
*Cc:* r-sig-mixed-models <r-sig-mixed-models at r-project.org>; Harold Doran
<harold.doran at cambiumassessment.com>; Ben Bolker <bbolker at gmail.com>
*Subject:* Re: [R-sig-ME] var(ranef(Random Effect)) not the same as the
variance component



First of all, thank you all for your valuable input.



Dimitris,



Thank you I upvoted your answer on CV as well. But please help me
understand a few things.



1- By D matrix, you mean the G matrix shown in:
https://bookdown.org/marklhc/notes/simulating-multilevel-data.html#linear-growth-model



2- When you say variance components in the output are prior values, can
you tell me how these prior values are obtained? I guess from the data
itself, but how exactly (do we run individual models first to see how much
intercepts and slopes vary & co-vary and take those as prior)?



3- Harold above noted that: "The conditional means of the random effects
are E(Y|X) and hence their variance is only one portion of the total
variance [i.e., var(y)]." I'm not sure how this directly relates to my
question in this thread?



Thank you,

Simon









On Tue, Sep 8, 2020 at 3:47 PM Harold Doran <
harold.doran at cambiumassessment.com> wrote:

To add a little notation to this, we can use law of total variance, var(y)
= E(var(Y|X)) + var(E(Y|X)). The conditional means of the random effects
are E(Y|X) and hence their variance is only one portion of the total
variance.

-----Original Message-----
From: R-sig-mixed-models <r-sig-mixed-models-bounces at r-project.org> On
Behalf Of D. Rizopoulos
Sent: Monday, September 7, 2020 11:02 PM
To: Simon Harmel <sim.harmel at gmail.com>; r-sig-mixed-models <
r-sig-mixed-models at r-project.org>
Subject: Re: [R-sig-ME] var(ranef(Random Effect)) not the same as the
variance component

External email alert: Be wary of links & attachments.


Yes, you do not expect these two be the same. The variance components are
the prior variances of the random effects, whereas var(ranef(model)) is the
variance of the posterior means/modes of the random effects.

Best,
Dimitris


Dimitris Rizopoulos
Professor of Biostatistics
Erasmus University Medical Center
The Netherlands