Hello,

I'm working with a relatively simple weighted LMM. The response is
estimated area of vegetation for a given site. The predictors include a
fixed slope and intercept over time, with a random intercept for site (23
sites, 6 time points [years,centered by mean]). I have an estimated
standard error of area for each site.

When I fit the unweighted model: fit=fit=lmer(value~cyear + (1|site),
data=dat, REML=FALSE, control=list(maxIter=5000)), I obtain
reasonable-looking results and as a diagnostic, I compared
sd(ranef(fit)[[1]]) to the reported (estimated) value from the fit, and
they were very close to one another.

When I fit the weighted model: fitw=lmer(value~cyear + (1|site),
weight=1/se/se, data=dat, REML=FALSE, control=list(maxIter=5000)), the fit
produces an estimated SD of the RE for site that is an order of magnitude
lower than sd(ranef(fitw)[[1]]) (.013316 vs. .1222606 for summary(fitw)
and sd(ranef(fitw)[[1]]), respectively).

I have fit both models in ADMB and obtained satisfactory results, with
respect to comparison of fixed-effect estimates between lmer() and ADMB and
estimates of random effects between lmer() and ADMB. The variance component
estimate from lmer() matches that of ADMB for the unweighted model, but not
the weighted model.

Is lme4 doing something else to the variance component estimate when
weights are used, or is this an error in how it is reported? lme4 appears
to estimate everything correctly, but I am not sure it is reporting what I
think it should be reporting for the variance component.

If anyone wants to test it out, the data are here:
http://students.washington.edu/cgast/Fig3dat.csv, and "cyear" is computed
as year-mean(unique(year))

Thanks,

Chris Gast








-----------------------------
Chris Gast, Ph.D.
cmgast@gmail.com

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