CLME stands for Constrained Linear Mixed Effects. I wrote this R package (CRAN link) during my postdoctoral work at NIEHS.
The fundamental idea is similar to the Jonckheere–Terpstra or any other test for ordered alternatives: If the treatment groups are ordinal, then a trend of some sort may be of interest. If a researcher has such a hypothesis, they can not only test for the ordered alternative, but they can constrain the estimation to respect the order from the alternative hypothesis.