My only suggestion would be to write some R code that calls the function of lme4 that you want when you want it. However, you might have to modify the existing package's code. My experience is it is difficult to modify someone else's R function. However it can be done. If you try to go that route you are advised to discuss this with the lme4 package maintainer before you start. May the force be with you. David Booth PS Note that you usually can't just combine two parts of a model like this because the usually optimize different things. Good luck.

Thanks a lot, David... I know that this approach has been used in the software MLwiN (University of Bristol). However, I wanted to implement it in R. And, as you say, it does not seem easy.

Hi Fernando Bruna Quintas , I am not sure if I follow, but if you want to input the model, like beta1-hat x1_i + beta2-hat x2_i, where the beta1-hat and beta2-hat are known, then could you use I(beta1 * x1 + beta2*x2). (note, this font I am seeing is bad, the character before the left parenthesis is capital EYE (for identity). Or just create a new variable using the predictions from the previous model.

Thank you Daniel Wright. I think that your suggestion might work. The idea is to to use instrumental variables to estimate the fixed parameters and in a second stage to keep those estimated coefficients but using the original endogenous explanatory variable to estimate the random part of the model. If I create a new variable using the predictions from the previous stage I might calculate Y-Yhat and use those residuals to estimate the random part. Is that what you mean?. It is simple, but it can work!

Yep, that is what I mean. The identity function is really useful when writing regression formula. Actually, I have Fox and Weisberg's book on my lap at the moment. they say: "The identity or inhibit function I(), which returns its argument unaltered, may be used to protect arithmetic expressions in model formulas" (p 236). It is a good book to have on one's lap when doing a regression.