Dear R-experts,

I am working with generalized linear mixed models in lmer and have a
question on the interpretation of variance components.  Specifically,
I would like to know how do we estimate the residual variance for random
effects when the value reported for the
residual error represents a scale parameter.

In lme4, The summary statement for a random intercept model gives me
something like:

 Random effects:

 Groups   Name        Variance Std.Dev.

 Transect (Intercept) 0.074105 0.27222

number of obs: 70, groups: Transect, 10

Estimated scale (compare to  1 )  1.053643

 What I'd like to know is the % of total variation explained by the random
variation in intercepts; i.e., var(intercept) / [var(intercept) +
var(residual)].

 A search on the previous posts in R -sig led me to read that
the residual variance of a glm or glmm with logarithm link is defined as
(pi^2)/3.  As such,  if the output from model run in lmer  gives  'Estimated
scale (compare to
1)', how would I estimate the residual variance? .  Do I have to multiply
the reported scale parameter (but not the variance components of
the random terms) by (pi^2)/3 to arrive at the actual residual variance.

And  if so, do I have to make  any changes to the variance components of the
random terms for the intercept (Transect).

 Thanks for any helpful suggestions !
Byju
Graduate Student, FNR, Purdue University

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