I'm looking for opinions on good current practice testing linear mixed effects models. As an unexpected result of my life choices, people are now often asking me questions about mixed models, and I want to be able to give good advice, or at least correct advice. Advice that steers people away from pits full of sharp spikes for people with a somewhat fuzzy understanding of what they are doing. I care particularly about the validity of tests on small datasets.

I would very much appreciate if you could point out any problems in what follows:

From my reading, Kenward-Roger tests are very good, with Satterthwaite tests usually also fine and faster to calculate. We only ever need to fit REML models now, as these tests are based on a restriction matrix rather than comparing two models with a likelihood ratio test. Older advice about sometimes using REML models and sometimes using ML can be disregarded (at least for linear mixed models).

In R, this can be done using lmerTest and emmeans. emmeans can also be used to get confidence intervals for most things I might be interested in. R code examples (section 8).

(I was a bit sad that multcomp doesn't support the Kenward-Roger method, as it would be nice to be able to get confidence intervals for arbitrary linear combinations of coefficients. It looks like I could use pbkrtest, but pbkrtest is a bit intimidating.)

I suspect there is a sub-population of statisticians where these sorts of choices don't really matter: they have plenty of data, all their random factors have many levels. The difference between REML and ML is negligible. Treating t statistics as z statistics is fine. Likelihood ratio tests on ML-fitted models are fine. It all works nicely for generalized linear mixed models too. Do you resemble this?

Or should I tell people to go Bayesian and use rstanarm?