[R] Lmer with weights

[Gregor Gorjanc]

Hello!

I would like to use lmer() to fit data, which are some estimates and 
their standard errors i.e kind of a "meta" analysis. I wonder if weights 
argument is the right one to use to include uncertainty (standard 
errors) of "data" into the model. I would like to use lmer(), since I 
would like to have a "freedom" in modeling, if this is at all possible.

For example we can take schools data by Gelman from R2WinBUGS package. 
As you can see bellow use of weights argument did not had influence on 
results.

I do not know if my specification of weights i.e. 1 / sd^2 is ok. Under 
least squares one minimizes sum(e^2_i) or sum(w_i * e^2_i) with weighted 
LS. If I consider that \sigma_i represents uncertainty in my "data" then 
e'_i = e_i / \sigma_i and we minimize sum(e'^2_i) = sum((e_i / 
\sigma_i)^2) = sum(e_i * \sigma^-2_i). Therefore weights i.e. w_i are 
equal to 1 / \sigma^2_i.

Can anyone help me with this issue?

Thank you very much!

 > library("R2WinBUGS")
 > data(schools)
 > schools
 > attach(schools)
 >
 > ## Fit simple model without "weights"
 > lmer(estimate ~ 1 + (1 | school))
Linear mixed-effects model fit by REML
Formula: estimate ~ 1 + (1 | school)
     AIC    BIC  logLik MLdeviance REMLdeviance
  58.882 59.041 -27.441     59.278       54.882
Random effects:
  Groups   Name        Variance Std.Dev.
  school   (Intercept) 80.4     8.97
  Residual             30.1     5.49
# of obs: 8, groups: school, 8

Fixed effects:
             Estimate Std. Error t value
(Intercept)     8.82       3.72    2.37

 > ## Fit simple model with "weights"
 > lmer(estimate ~ 1 + (1 | school), weights = ~ 1 / (sd^2))
Linear mixed-effects model fit by REML
Formula: estimate ~ 1 + (1 | school)
     AIC    BIC  logLik MLdeviance REMLdeviance
  58.882 59.041 -27.441     59.278       54.882
Random effects:
  Groups   Name        Variance Std.Dev.
  school   (Intercept) 80.4     8.97
  Residual             30.1     5.49
# of obs: 8, groups: school, 8

Fixed effects:
             Estimate Std. Error t value
(Intercept)     8.82       3.72    2.37

-- 
Lep pozdrav / With regards,
     Gregor Gorjanc

----------------------------------------------------------------------
University of Ljubljana     PhD student
Biotechnical Faculty
Zootechnical Department     URI: http://www.bfro.uni-lj.si/MR/ggorjan
Groblje 3                   mail: gregor.gorjanc <at> bfro.uni-lj.si 

SI-1230 Domzale             tel: +386 (0)1 72 17 861
Slovenia, Europe            fax: +386 (0)1 72 17 888 

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"One must learn by doing the thing; for though you think you know it,
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