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

vito muggeo vito.muggeo at giustizia.it
Fri Aug 30 11:20:34 CEST 2002

See the rmeta package on CRAN (the metaDSL() function would do what you are
looking for).

i)In the model estimation, the estimated coefficients beta have to be
weighed by the inverse of their variance (the smaller the variance, the more
accurate the estimated beta, the more important its influence on the pooled
estimate)
ii) As far as I know, it makes no sense to set no.group=no.observations;
otherwise you could not estimate the intra-group variance.

best,
vito

----- Original Message -----
From: "J.R. Lockwood" <lockwood at rand.org>
To: <r-help at stat.math.ethz.ch>
Cc: "J.R. Lockwood" <lockwood at rand.org>
Sent: Thursday, August 29, 2002 8:00 PM
Subject: [R] lme() with known level-one variances

> 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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