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The documentation says that Kenward Roger is only available for lme models (here); this is a simple typo but led me down the wrong track for quite a while!

standardized generalized variance

  • Where is the standardized generalized variance approach documented? It's not easily located in Jaeger 2016.
  • Handling of crossed models (cf this issue)

My models have multiple random effect terms/grouping variables (roughly speaking, flor_realms in the example below is the largest-scale/smallest number of levels (n=6, mean 103.3 obs/block); biomes is smaller-scale but crossed with flor_realms (14, 44.3); and biome_FR (55, 11.2) represents the interaction between these two sampling levels. In the paper, I see (below eq 10)

\hat\Sigma is the estimated covariance matrix for the pseudo otucomes having a block diagonal structure with subject-specific estimated covariance matrices \hat\Sigma_i = Z_i \hat\Sigma_b Z'_i + \hat W_i{-1}, i=1, ..., n constituting the blocks

However, my Sigma is not block-diagonal because it combines information from three different sampling levels ... r2beta.lmerMod appears to choose the last grouping variable automatically to do the block size/samples per block calculations (which if I recall correctly is always the grouping variables with the fewest levels given lme4's internal rearrangements). `

The block size info seems to be used in two places:

(1) in calc_sgv(). I see that ?calc_sgv says "calculates the standardized generalized variance for a block diagonal matrix", but I don't see SGV referred to anywhere in Jaeger et al 2017 (maybe there's a later reference?). As far as I can tell the definition of SGV is more generally

exp(determinant(SigHat,log=TRUE)$modulus/nrow(SigHat))

Could perhaps use this expression instead of calc_sgv() ?

More generally, I'm not sure why the computation is using SGV. I see that r2beta.lmerMod is internally converting SigHat (the full covariance matrix) to its SGV before calling cmp_R2. I'm not sure why ... ?

Instead of what's done in r2beta, cmp_R2 will (apparently) take SigHat either as a scalar or as a matrix ... the latter seems more general and closer in spirit to what the paper suggests ... ?

cmp_R2 (i.e., allowing for arbitrary contrasts) has a different setup/interface than r2glmm(..., partial=TRUE). Seems hard to use K-R ddf in a cmp_R2 context ?

issues with gamm4 models

gamm4 models are pretty terrible to work with for a variety of reasons:

  • call object is mangled to uselessness
  • the formulas and terms are not very useful; drop1 doesn't really work
  • I've resorted to setting up an interface where the user has to specify the partial terms manually, although I have a hack to guess it
  • hard to know what the null model should be (include smooth terms or not?)