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

[ben pelzer]

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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