LME as part of meta-analysis

Le vendredi 27 mars 2009 ? 15:30 -0700, mrint a ?crit :

Hi, I'm having a problem using LME and hopefully I can get some help.  Here
is what I'm doing:

I have a model like this:

yi = alpha + theta * xi + beta * zi + error, errors are normally distributed
mean 0, var sigma^2

xi and zi are generated from normal distributions within a specified range.  

True values of alpha, theta, beta and sigma^2 are chosen with a specific
mean and variane tau^2.

I have a function which generates the yi from the other variables, then a
function that does a linear regression using lm to create the estimates.  

I then want to use this data to do a meta-anaylsis with the above repeated
between 10-20 times.  Within this, I want to use lme to create estimates for
the average true value, sample mean and average standard error for alpha,
theta, beta and the respective tau^2 values for each of these.  For the lme
part, I'm using this

a<-summary(lme(alp~1,random=~1|alp, weights=varFixed(~staalp^2)))

This is the one for alpha.  This isn't producing the type of results I would
expect, can anyone see where I'm going wrong?  

(I suppose that your simulation aims to assess a specific model)

This, and closely related subjects, have already been discussed on this
very list. To make a long story short : lme doesn't (currently) accepts
means and variances of groups as an input, it needs individual data.
Someone (that should be Wolfgang Vischbauer, but I'm almost surely
mutilating his name's spelling ; apologies, Wolfgang !) has written,
specifically for meta-regression purposes, a "mima" function that does
what you're requesting. Wolfgang has stated his intentions to turn this
function into a full-fledged R package (with calling conventions closer
to what other regression functions use), but the "mima" function
available on his site still his 2 years old 0.4 version. For further
details, look for "mima" or for "meta-regression" in the list archives.
RSiteSearch() is your friend...

However, if what you're interested with is strictly speaking a
meta-analysis of 2-samples comparisons (i. e. your theta is scalar and
your x_i are logicals), (at least) two R packages available on CRAN are
built for this purpose : rmeta and meta. Both offer separate analyses
for boolean or continuous dependent variables (i. e. y_i logical or
continuous).

If your theta is scalar but your x_i is continuous (i. e. you're
meta-analysing a single regression coefficient), both package offer a
variant for meta-analysis of effects, that might be relevant for you.

A more general solution would be to enhance the forthcoming lme4 package
to accept an alternative specification of random effects
variances-covariances, which would allow "general" meta-regression. But
I understand that Douglas Bates has already way too much work and not
too much time on his hands, and I doubt he might be coaxed to work in
this direction right now...

A suggestion : you might forward your question to the "r-mixed-models"
SIG mailing list with some profit...

					Emmanuel Charpentier