[R-sig-ME] lme4 to get a vcov for fixed-effects variance

[wilson 1998]

Following the previous email to make it just text only questions: I�ll restate my questions:

Hi Ben Bolker,

I would like to know about some mechanism about vcov output from glmer model from here<https://cran.r-project.org/web/packages/lme4/vignettes/lmer.pdf>

So I am running a model using glmer under poisson model
fit1 = glmer(count~spp + (1|site),data=Salamanders, family=poisson)
using Salamanders data<https://www.rdocumentation.org/packages/glmmTMB/versions/1.0.2.1/topics/Salamanders> from glmmTMB package in R Studio

Then it could produce the variance covariance matrix about the fixed effects given below:, also since full=T it also gives the extra column and extra row to account for the random effect as well.

vcov(fit1,full=T)


I noticed in page 26 in section 5.1 in lme4 documentation (equation 54 and equation 55) from this link: https://cran.r-project.org/web/packages/lme4/vignettes/lmer.pdf#page=14&zoom=100,568,614


However, How do I reproduce the output for vcov manually? I know that under equation (55) it says that they could reproduce using chol2inv(RX) to represent R_X^-1 (R^T_X)^-1

I don�t get it how to produce the R_X, L(theta) ,R_ZX as well? It is stated that there could be Cholesky decomposition, but what if I would like to get this manually for each component?
The main point is that I would like to know how could the lme4 package get the output for the vcov(fit1,full=T). And in this case, I also would like to know how to extract R_X and R_ZX from the fit1?

Thankyou.

Regards,
Wilson



Below is the previous email with the comment

Your request to the R-sig-mixed-models mailing list

    Posting of your message titled "lme4 to get a vcov for
fixed-effects variance"

has been rejected by the list moderator.  The moderator gave the
following reason for rejecting your request:

"Could you please resend without the embedded text from the JSS paper?
(The mailing list is very old-fashioned and only likes plain-text
messages.) You can point to the specific section in the JSS paper
(e.g. "in section 5.1 'Theory underlying the output module', in the
first subsection 'Covariance matrix of the fixed-effect
coefficients').

If you could also clarify your question that would be useful: do you
want to know how RX is computed during the estimation procedure (see
eq 51 of the JSS paper), or how to extract it from the fit [which is
stated in the text you quoted], or ... ?

  sincerely
   Ben Bolker"

Any questions or comments should be directed to the list administrator
at:

    r-sig-mixed-models-owner using r-project.org


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