[R-sig-ME] var(ranef(Random Effect)) not the same as the variance component

[Simon Harmel]

Thank you, Harold.

1) `var(ranef(fm1)$Subject)` is the posterior variance of random effects or
their prior variance? (this was the point discussed so far in this thread)

2) Also, what about `mean(sapply(attr(ranef(fm1)$Subject,
"postVar"),function(x) x))`, what this expected variance represents in
words?

3) What does their sum represent? The total observed variance in random
deviations in intercepts of subjects?

Thank you very much

On Wed, Sep 9, 2020 at 1:48 PM Harold Doran <
harold.doran using cambiumassessment.com> wrote:

> 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 using gmail.com>
> *Sent:* Wednesday, September 9, 2020 11:53 AM
> *To:* D. Rizopoulos <d.rizopoulos using erasmusmc.nl>
> *Cc:* r-sig-mixed-models <r-sig-mixed-models using r-project.org>; Harold Doran
> <harold.doran using cambiumassessment.com>; Ben Bolker <bbolker using 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 using 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 using r-project.org> On
> Behalf Of D. Rizopoulos
> Sent: Monday, September 7, 2020 11:02 PM
> To: Simon Harmel <sim.harmel using gmail.com>; r-sig-mixed-models <
> r-sig-mixed-models using 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
> ________________________________
> From: R-sig-mixed-models <r-sig-mixed-models-bounces using r-project.org> on
> behalf of Simon Harmel <sim.harmel using gmail.com>
> Sent: Tuesday, September 8, 2020 1:22:15 AM
> To: r-sig-mixed-models <r-sig-mixed-models using r-project.org>
> Subject: [R-sig-ME] var(ranef(Random Effect)) not the same as the variance
> component
>
> Hello All,
>
> A very basic question. Generally, `var(ranef(Random Effect))` may not
> necessarily be the same as the variance component reported for that Random
> Effect in the model output, correct?
>
>
> Thank you all,
> Simon
>
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