Help understanding residual variance

But why is Greg Snow's response inadequate?

Restating his argument: ?In an LMM we are not estimating individual
random effects (means, slopes) and individual residuals, but variance
of random effects and variance of residuals. So there can be
differences between a subject's observed random effect and random
slope ?and conditional modes of the distribution of the random effects
(i.e., the point of maximum density), given the observed data and
evaluated at the parameter estimates.

I think your statistician's answer is a good argument that you must
not treat conditional modes as independent observations in a
subsequent analyses. For example, we showed with simulations that
correlations between conditional modes of slopes and intercepts are
larger than the correlation parameter estimated in the LMM (Kliegl,
Masson, & Richer, Visual Cognition, 2010).

Reinhold Kliegl

--
Reinhold Kliegl
http://read.psych.uni-potsdam.de/pmr2

On Tue, Mar 27, 2012 at 4:18 AM, Ista Zahn <istazahn at gmail.com> wrote:

Hi all,

I'm trying to understand what the residual variance in this model:

tmp <- subset(sleepstudy, Days == 1 | Days == 9)
m1 <- lmer(Reaction ~ 1 + Days + (1 + Days | Subject), data = tmp)
tmp$fitted1 <- fitted(m1)

represents. The way I read this specification, an intercept and a
slope is estimated for each subject. Since each subject only has two
measurements, I would expect the Reaction scores to be completely
accounted for by the slopes and intercepts. Yet they are not: the
Residual variance estimate is 440.278.

This is probably a stupid question, but I hope you will be kind enough
to humor me.

Best,
Ista