[R] meta-regression, MiMa function, and R-squared

Christian Gold c.gold at magnet.at
Mon Mar 12 13:34:53 CET 2007

Dear Wolfgang

Thanks for your prompt and clear response concerning the R^2.
You write:

> Note that the mima function does nothing else but fit the model with 
weighted least squares using those weights. So, you could actually use
"lm(y ~ x1 + ... + xp, weights=w)" and you should get the exact same
parameter estimates.  Therefore, "summary(lm(y ~ x1 + ... + xp,
weights=w))" will give you R^2.

Is this really true? I thought that "in weighted regression the
/relative/ weights are assumed known whereas in meta-regression the
/actual/ weights are assumed known" (Higgins & Thompson, 2004,
"Controlling the risk of spurious findings from meta-regression",
Statistics in Medicine, 23, p. 1665). Also, I did calculate my
regression problem with lm using inverse variance weights before I
discovered your function, and have compared the results now. The
regression coefficient was the same, but the confidence interval was
wider with mima. Furthermore, the CI with mima depended on the absolute
size of the weights (as I assume it should do), whereas with lm it did
not. Can you explain?



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