# [R] lme() with known level-one variances

J.R. Lockwood lockwood at rand.org
Thu Aug 29 20:00:59 CEST 2002

Greetings,

I have a meta-analysis problem in which I have fixed effects
regression coefficients (and estimated standard errors) from identical
models fit to different data sets.  I would like to use these results
to create pooled estimated regression coefficients and estimated
standard errors for these pooled coefficients.  In particular, I would
like to estimate the model

\beta_{i} = \mu + \eta_{i} + \epsilon_{i}

\eta_{i} ~ iid N(0,\tau^2) and independent of the \epsilon_{i}, the
latter themselves being independent with variances assumed known and
equal to the squared standard errors reported in the regression
output.

I would like to use lme() to estimate \tau^2 by REML, and also get a
sensibly weighted estimate for \mu from the fixed effects output.  I
am not sure how to do this.  I have tried

lme(fixed=beta~1,random=~1|group,weights=~beta.v)

where "beta" are my coefficients, "group" is a trivial factor
indicating that each observation is its own group, and "beta.v" are
the squared standard errors.  Whatever I get out of this doesn't make
sense to me, and I suspect that I have specified the model
incorrectly.

Incidentally, if I just run the simple unidentifiable model

lme(fixed=beta~1,random=~1|group)

lme() somehow manages to produce estimates of the two variance
components, although the estimated confidence intervals are huge and
contain zero.  If I square and sum the estimated variance components,
I do get the sample variance of my regression coefficients, but why
that particular parceling of variance was chosen as opposed to any
other with the same property eludes me.

Here are my specs:
platform i686-pc-linux-gnu
arch     i686
os       linux-gnu
system   i686, linux-gnu
status
major    1
minor    5.1
year     2002
month    06
day      17
language R

Thanks in advance for your help -- I've learned a ton of statistics
and computing on this list.

J.R. Lockwood
412-683-2300 x4941
lockwood at rand.org
http://www.rand.org/methodology/stat/members/lockwood/

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