[R-sig-ME] Trying to align lmer output with Robinson's BLUP is a good thing

[Ben Bolker]

    You can get most of the answers to these questions from the JSS 
paper (vignette("lmer", package = "lme4")).

   X: getME(fitted_model, "X")

   Z: t(getME(fitted_model, "Zt"))

   I believe G is

Lambda <- t(getME(fitted_model, "Lambdat"))

G <- crossprod(Lambda) ## or maybe tcrossprod()?

R <- diag(nobs(fitted_model))

   (but you should double/cross-check with the JSS vignette, I didn't 
look at the definitions in the Robinson paper super-carefully)

   At present lme4 only allows predictions that are either completely 
unconditional (re.form = NA) or conditional on the b values (re.form = 
NULL), not conditional on the y-values from the new level and the 
top-level estimates (sigma^2, theta -> G). You can follow the machinery 
in Robinson's paper or (as you pointed out in another e-mail) follow the 
machinery here: 
https://github.com/drizopoulos/JMbayes/blob/master/R/dynPred_lme.R but 
adapted for lme4

   This would be a good idea to include in lme4, if anyone wants to 
implement and make a pull request :-)

On 2023-04-15 8:16 p.m., Ravi Varadhan via R-sig-mixed-models wrote:
> Hi,
>
> I am trying to understand the model fitting of lmer() with the aid of GK Robinson's 1991 paper "BLUP is a good thing."  I am trying to align the lmer() output with Robinson's notation.
>
> I have a few questions in this regard.
>
>    1.  How can I get matrices X and Z from lmer?
>    2.  How do I obtain the variances G and R?
>    3.  For a new subject (x*, z*), is it possible to obtain BLUP predictions of x*\beta + z*u as shown in Robinson's paper? When I try to do this using predict.merMod, it complains that new levels are not allowed for conditional prediction.
>
> Thank you,
> Ravi
>
>
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>
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