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

[Simon Harmel]

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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