[R-sig-ME] Size/metric of variance components in lme and lmer

[Stuart Luppescu]

Hello, I have run two analyses, each with the same data set and
predictors. One is a nested model run with lme; the other is a
cross-classified model with lmer. The only difference between the two
models is the added random effect. For example, the nested model
statement looks like this:

nested.lm3 <- lme(final.points ~ -1 + gr10 + gr11 + gr12 + per1 + per2 +
per4 + per5 + per6 + per7 + per8 + per9 + per10 + per11 + per12 +
                  cblackd + casiand + clatinod + cmale + cssoc + cscon +
cold4gr  + cmlatent8 + computer +
                    ...
               jourlsm,
                  data=all.subj, random = ~ 1|sid, na.action=na.omit)

The cross-classified model looks like this:

lm4c <- lmer(final.points ~ -1 + gr10 + gr11 + gr12 + per1 + per2 + per4
+ per5 + per6 + per7 + per8 + per9 + per10 + per11 + per12 +
                  cblackd + casiand + clatinod + cmale + cssoc + cscon +
cold4gr  + cmlatent8 + computer +
                  ...
                  jourlsm +
            ( 1 | sid) + (1 | tid), data=all.subj,  REML=F, verbose=T)

The variance components for the nested model are:
Random effects:
 Formula: ~1 | sid
        (Intercept)  Residual
StdDev:   0.8826577 0.9259174

for the cross-classified model:

 Groups   Name        Variance Std.Dev.
 sid      (Intercept) 0.75426  0.86848 
 tid      (Intercept) 0.39601  0.62929 
 Residual             0.68535  0.82786 

If we square and sum the variance components for the nested model, the
total variance is about 1.64. For the cross-classified model, the total
variance is about 1.84. Where did the additional variance come from?

Should I just interpret the size of the variance components on a
relative scale, are the units different, or what?

-- 
Stuart Luppescu -*-*- slu <at> ccsr <dot> uchicago <dot> edu
CCSR in UEI at U of C