Singularity in Power Simulations

[palday]

I think this is something we should document and discuss. Two important aspects:

1. Simulating from a singular model means that the ground truth of the covariance matrix will also be singular.
2. As @kliegl suggested, a certain proportion of singular fits in a power analysis is indicative of a sample size that's too small for your proposed design. There's some fine print here about whether or not you care about the variance components or can safely assume they're zero (and thus omit them) or whether those are the things you're trying to estimate. Maybe this is also a spot where the parametric bootstrapped confidence interval for the variance component may be misleadingly small and close to zero.