Power Calculations in Longitudinal Mixed Effects - from two measurements to three measurements

@JorgeTeixeira when analyzing data with baseline (pre-treatment) and multiple post-treatment time points, I prefer to use an AR(1) structure as a starting point. It logically/clinically makes sense and is why there is the long standing issue of using lme4.

If, for some reason, your actual data do not meet those assumptions, you can then explore alternatives, but if you need to pre-specify these details in an SAP, AR(1) is what I would use.

With respect to the older lme() function in the nlme package that is part of Base R + Recommended packages, the description of the “correlation” argument in the documentation is as follows:

an optional corStruct object describing the within-group correlation structure. See the documentation of corClasses for a description of the available corStructclasses. Defaults to NULL, corresponding to no within-group correlations.

Apparently, over time, the last sentence regarding the default has led to confusion, with some interpretations being unstructured and others being independence.

Finding what would reasonably be considered the definitive reference from 1998 by Jose and Doug:

https://www.stat.cmu.edu/~brian/720-2007-source/week07-08-ideas/pinheiro98mixedeffects-Sguide.pdf

on the bottom of page 19 is the following:

The optional argument correlation is used to specify a correlation structure and the optional argument weights is used for variance functions. By default, the within-group errors are assumed to independent and homoscedastic.

so that might help to mitigate some of the confusion. It is also why I have never used the default, and prefer to explicitly define these details.