[R-sig-ME] Full Information matrix or Variance Covariance matrix in glmmTMB

[Ben Bolker]

On 2023-11-07 3:46 p.m., Olaifa, Julius wrote:
> I am trying to obtain the Fisher Information matrix or variance covariance matrix for a glmmTMB model. The model implements model$sdr$cov.fixed​  which returns the variance covariance matrix between the regression parameter coefficient (Beta)​and the dispersiom parameter (phi).
> I however want to obtain the variance covariance matrix of both the fixed parameters and random effect covariance estimates (Beta, phi, Sigma)​

  I think vcov(., full = TRUE) will get what you want.

   I You should be able to get this by inverting the results of 
TMB::sdreport(..., getJointPrecision = TRUE), as for example:


library(glmmTMB)
data("sleepstudy", package = "lme4")
m1 <- glmmTMB(Reaction ~ Days + (Days|Subject), sleepstudy)
colnames(vcov(m1, full = TRUE))

                 cond1                  cond2                   disp
          "(Intercept)"                 "Days"        "d~(Intercept)"
                 theta1                 theta2                 theta3
"theta_Days|Subject.1" "theta_Days|Subject.2" "theta_Days|Subject.3"

   If you want the joint precision/covariance matrix that also includes 
the BLUPs/conditional modes:

ss <- TMB::sdreport(m1$obj, getJointPrecision = TRUE)
h <- solve(ss$jointPrecision)

    You should be aware that this could get ugly for large problems; the 
joint precision matrix (i.e., the inverse of covariance matrix) is 
sparse/well-structured, but the joint covariance matrix is dense.


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-- 
Dr. Benjamin Bolker
Professor, Mathematics & Statistics and Biology, McMaster University
Director, School of Computational Science and Engineering
(Acting) Graduate chair, Mathematics & Statistics
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