[R-sig-ME] Measurement error for mixed models

[Viechtbauer, Wolfgang (SP)]

Hi Krzysztof,

This can be done with lme(). Let si2 denote the known variance of observation i. With varFixed(), you can specify that the error variances are known up to a proportionality constant, sigma^2. With lmeControl(sigma=1), you can fix that proportionality constant to 1, so the error variances are equal to s2i. Then add random effects for each row of the dataset. That will be your s^2. So, putting this all together:

dat$id <- 1:nrow(dat)
lme(yi ~ x1 + ..., random = ~ 1 | id, 
    weights = varFixed(~ si2), 
    control = lmeControl(sigma = 1), 
    data = dat)

Interestingly, this is identical to what is done in meta-analysis in the 'random-effects model', where we have known sampling variances for the outcomes and we add a random effect for each row (i.e., study) to the model. You might find this of interest:

http://www.metafor-project.org/doku.php/tips:rma_vs_lm_lme_lmer

But also read the note at the end -- there is (was?) some issue with lme() when fixing sigma to a constant. Not sure if this has been fixed in the meantime.

Best,
Wolfgang

-----Original Message-----
From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces using r-project.org] On Behalf Of Krzysztof Bartoszek via R-sig-mixed-models
Sent: Wednesday, 11 September, 2019 16:02
To: r-sig-mixed-models using r-project.org
Subject: [R-sig-ME] Measurement error for mixed models

Dear all,
As far as I managed to see the weights parameter in nlme::lme(), mgcv::gamm(), gamm4::gamm4(), can be used to pass some specific residual variance structure based on nlme's varFunc class. I was wondering if the following variance structure is possible to be obtained from the already implemented instances in varClasses, or I will need to code it myself.

I want the variance of the response for observation i to be of the form v_i^2 = s^2 + s_i^2, where s^2 is a common for all observations unknown variability and s_i^2 is known, individual specific measurement error variance (can be 0).

Thank you
Best wishes
Krzysztof Bartoszek