Closed AbigailLoe closed 6 months ago
@AbigailLoe can you say more about Wald test undercoverage? Do you have a citation? Is this under coverage only for small group counts, e.g., is it solved if you use CR-2 as in the clubSandwich package @jepusto wrote? (Note that clubSandwich
doesn't work with WeMix.)
@pdbailey0 Gałecki, A., Burzykowski, T. (2013). Linear Mixed-Effects Model. In: Linear Mixed-Effects Models Using R. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3900-4_13 is a citation for one (page 263 specifically, covers the under estimation of likelihood based methods for uncertainty in parameter estimation). My guess is it is solved with a sandwich estimator to account for the extra variability in estimation, but I am not sure.
WeMix
uses CR-0 variance estimation, following Wolter's (2007). Introdution to Variance Estimation. 2nd edition. Springer. Chapter 6 is where the Taylor series approach is described. Though you can also find it in the WeMix Vignette in a section titled, "Variance Estimation." which gives a Binder (1983) citation that is a bit easier to read.
If you're interested in an S4 object being returned, that seems like a relatively simple fix and we are happy to entertain pull requests.
What are best practices for estimate confidence intervals for the fixed effects model parameters using WeMix? Any advice or directions to pertinent documentation would be very helpful. I am mostly concerned about undercoverage due to Wald-type estimates being insufficient characterizations of variance, but I also would like to avoid needing to bootstrap in my simulations, particularly since I would need to do so by hand.
Alternatively, there are packages that do the bootstrapping of mixed effects models, but WeMix outputs "WeMix" objects. If there's some way to coerce a WeMix model into an S4 object, or an object of the same type as lmer outputs, that would be really helpful as well.