I would like to obtain tau2 estimation using REML by making use of PROC MIXED procedure in SAS to compare the estimation result obtained from rma function in R.

I have used the following SAS code;

proc mixed data= dat method=reml;
class pubid;
weight Weight;
model Effectsize=  / cl solution; 
random intercept / subject=pubid;  
parms (1)(1)/ hold=2; 

Here the data consists of Effectsize, pubid as well as Weight(which is calculated from 1/variance for each study)

This code gives the same tau2 estimate as seen in the results from rma function but I am not really clear how this weight function specified in SAS procedure is working. Could you please explain what role does it exactly play in the tau2 calculation? I am confused especially because weight is said to 1/ Se2+tau2reml in most of the books where tau2 reml estimation is explained...

I read that since here I don't have repeated statement specified in my SAS procedure, WEIGHT statement basically operates exactly like PROC GLM and replaces X’X and Z’Z with X’WX and Z’WZ, where W is the diagonal weight matrix. I am not really clear with what is meant by this. Could you please clarify?

Many thanks in advance.


If you go to the documentation for the WEIGHT statement in PROC GLM there is a good explanation. The key bit is at the beginning:

When a WEIGHT statement is used, a weighted residual sum of squares: $$\sum{w_i(y_i - \hat{y}_i)^2}$$ is minimized, where $w_i$ is the value of the variable specified in the WEIGHT statement, $y_i$ is the observed value of the response variable and $\hat{y}_i$ is the predicted value of the response variable.

So, it basically just changes what is minimized. It does the same in MIXED unless there is a REPEATED statement. If you do have a REPEATED statement then WEIGHT also changes the R matrix.


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