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/ggorjanGroblje 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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