[R-sig-ME] random effect variance greater than output variable variance

[J.D. Haltigan]

This is the between/within variance issue in multilevel modeling. Take a
look at:

Hamaker EL, Muthén B. The fixed versus random effects debate and how it
relates to centering in multilevel modeling. *Psychological Methods* 2020;
*25*:365.


Bell A, Fairbrother M, Jones K. Fixed and random effects models: making an
informed choice. *Quality & Quantity* 2019;*53*:1051–74.

On Thu, Nov 10, 2022 at 3:31 AM ben pelzer <benpelzer using gmail.com> wrote:

> Dear Norman,
>
> Sorry, I mixed up things. In case of a random slope of an X variable it can
> happen that the variance across "schools", say, is very high because it
> refers to the variance between "schools" for X=0. But you do NOT have
> random slopes of disease and rainfall, so my remark was not appropriate.
>
> With the summary results, I now see what your problem is, and I have no
> good answer. One thing however is this. The three random intercept
> variances of location etc. refer to any given combination of X, R1 and R2.
> I believe these should be interpreted as conditional variances, conditional
> on the values of X, R1 and R2, that is. This is different from the total
> variance of your dependent Y, which you get by using var(Y). Suppose you
> run a null-model, with only the random effects and no fixed-effect
> predictors X, R1 and R2, then you could compare the sum of the four
> variances (incl. the residual variance ) with the one obtained by var(Y).
>
> In general, these two variances can differ. In a "schools" example with
> different nr. of pupils in a number of schools, the null-model variance
> better suits the two-stage sampling design: at random sample schools,
> within each school sample pupils.
>
> Thanks for pointing me to the blog of Ben Bolker, this is great and useful
> stuff.
>
> Cheers, Ben.
>
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>
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