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May 30, 2016 at 8:12 comment added usεr11852 Regarding the naming: "realisation of random effects" should be a first thing to check. I do not think it has a particular name; it just a by-product of the variance components estimation.
May 30, 2016 at 8:07 comment added usεr11852 Glad I could help. Please read the JSS paper Fitting Linear Mixed-Effects Models Using lme4 by Bates et al. in detail. This should answer most questions on this matter. In particular check the arguments getME(fm1,'Lambda') as well as the method VarCorr. Yes, lmer do not give the covariance factor directly but that is because it is never really uses it. It uses relative covariance factors. (In general, lmer is fast because it turns all the LME model estimation into on big sparse Cholesky decomposition.)
May 30, 2016 at 0:34 comment added Tay Shin oops I've just found out that you already cited the paper :) !
May 30, 2016 at 0:11 comment added Tay Shin @usεr11852 wow Thanks for the fast reply! :D However, I don't think [getME] function in lme4 doesnt support for the covariance factor. Also, could I ask one extra question? is there any "name/term" for above equation or can you please give me a terminology so that I could look up for the some document that drive above equation. Thank you very much :D
May 29, 2016 at 20:08 comment added usεr11852 @TayShin: I guess you mean $\Psi_\theta$ (psi) and not $\Phi$ (phi) right? In general: $\gamma_i \sim N(0,\Psi_\theta)$. Yes you are correct, this is of dimensions $q \times q$. The cited paper explains this in detail. You can get these using the getME function (eg. getME(fm1,'Z'), etc.) See ?getME and methods(class="merMod") for mode lme4 specific calls.
May 29, 2016 at 18:24 comment added Tay Shin @usεr11852 Will you please elaborate more on phi value(theta)? It seems the phi value has the dimension of (n x n ) where n is the number of grouping factor for random effect. How could I get those values in R by using lme4 package?.
Feb 18, 2013 at 17:09 comment added usεr11852 Yes; taking in account what you said on the other comment also. (what you mean about "When I obtain the likelihood, I used the random effect."?) If what you want is the predictions for the measurements you already have then you want to add the random intercept.
Feb 18, 2013 at 14:52 comment added Günal I am not using the package programmes in R. I am using the vector of regression coefficients and design matrix. When I obtain the likelihood, I used the random effect. So, do I need to calculate the fitted values using random effect?
Feb 15, 2013 at 19:53 history edited usεr11852 CC BY-SA 3.0
Added mention to why someone might want to use the "mean response" as pointed out by S.L.
Feb 15, 2013 at 17:29 history answered usεr11852 CC BY-SA 3.0