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Clarifications on implementation of lmer (lme4) in R -weights

I was reviewing the documentation on lmer (lme4) found here:
http://cran.r-project.org/web/packages/lme4/vignettes/lmer.pdf. The
document refers to W^-1 as "known
prior weights".

Is this "weight" the same concept as using weights in a model "lm"?

I did some testing between the lme and lmer (with REML estimator; random
slope and intercept).

Without any weights, I get the same estimates for lme and lmer. However,
when I include a weight given by inverse of the sample size by ID. I get
very different results.

I think I may be interpreting these weights differently.

Sincerely,
Christian
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