I would like to share some of my thoughts when trying to improve the model fitting time of a linear mixed effects model in R using the lme4 package. <
R
lme4
We have implemented random intercepts regression assuming compound symmetry in the R package Rfast. The command is rint.reg. It is 30+ times faster than the corresponding lme4 function. I do not know if this helps, but just in case.
https://cran.r-project.org/web/packages/Rfast/index.html