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
________________________________
From: R-sig-mixed-models <r-sig-mixed-models-bounces at r-project.org> on
behalf of Simon Harmel <sim.harmel at gmail.com>
Sent: Tuesday, September 8, 2020 1:22:15 AM
To: r-sig-mixed-models <r-sig-mixed-models at 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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