[R-sig-ME] Varying random variance from random slopes model?

[Mitchell Maltenfort]

Sorry if this one seems confusing.  I’ll be as clear as I can.

I was originally using random intercept LMM to generate a Z score as the
difference between the predicted conditional mean from fixed effects and
the real observation, divided by the SD from the combined residual and
random intercept variances.

I’m now adding random slopes, plural.  AIC suggests much better fit.  But
here’s the problem:

I had naively assumed I could estimate a random effects variance dependent
on the slope terms by estimating the sum of the random intercept plus the
random slope times the value for each of the slope parameters, and then the
variance of that sum across the population.  (I’d then look for a curve
that described this variance as a function of the slope terms.)

However, I had also had the assumption that the SD term for random
intercept in the LMM summary (using lmer) was the standard deviation of the
random effects for intercept.  I now realize that isn’t the case, as the
summary from lmer describes the multivariate Gaussian distribution giving
rise to the random effects, not the random effects themselves.  (Entirely
possible I have that wrong, too!)

So my question is, finally, is there a way to calculate a realistic SD
estimate that varies with the slope parameters?  I was hoping to plug that
into my Z score calculation.

I’m probably missing something basic..

Thanks in advance!

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