Omitted Topics

Here's a brief list of topics that we didn't have space to cover adequately in the paper:

general areas:

  • dependence of estimates, inference, etc. on transformation of parameters (e.g. fitting $\log(b)$ instead of $b$). This applies in general to Bayesian methods (provided that we look at the mean and credible intervals, and not the mode/median/quantiles). It also applies to the Wald test (Molenberghs and Verbeke).
  • pedigree/breeding value testing (huge literature in animal breeding etc., some work by Bates to try to get the pedigree framework to connect with lme4.
  • spatial and temporal GLMMs. Very interesting question, one we had absolutely no space to go into. The general answers to these questions seem to be:
    • use quasi-methods if possible? (e.g. Gotway and Stroup 1997)
    • use generalized estimating equations (Dutch seabird stuff)
    • use MCMC
    • it has also been suggested to use Fourier decomposition, splines, etc. as more flexible (and efficient) ways of accounting for spatial covariation — rather than the
    • software:
      • lme4 doesn't (and won't for a while) deal with spatial/temporal autocorr.
      • nlme does, but that's for LMMs and NLMMs (not GLMMs) only.
      • PROC GLIMMIX? (don't know about NLMIXED)
      • geoRglm
      • WinBUGS/GeoBUGS?
    • books: Schabenberger and Gotway, Waller and Gotway, (xxx and Diggle model-based geostats book)
    • papers: [1]

open questions:

  • should one use a Wald Z/$\chi^2$ test (not t or F) for GLMMs in the absence of overdispersion? Why/why not? (Why: saves having to figure out 'denominator/residuall df'. Why not: I thought I saw this somewhere, and Littell et al 2006 mention it in passing)
  • Thinking about the connection between 0-1 (effective df for a LRT on a single random factor) vs 1 to N-1 (effective df for a random factor considering amount of shrinkage). Think this is also connected with issues about "focus of inference" (Spiegelhalter et al 2002)/ "conditional AIC" (Vaida and Blanchard 2005). Fabian Scheipl said:

I think this is connected to the question of whether you are looking at the marginal or conditional interpretations of the random effects (and , correspondingly the marginal or conditional AIC, see f.e. Florin Vaida's work) - if you marginalize over the realizations of the random effects you are really looking at a single additional paramter in a simple random intercepts model (e.g. : the variance of the random intercepts), but if you condition on the realizations of the random effects the increase of the degrees of freedom of your model by including that random intercept really depends on the amount of regularisation of the random intercepts, that is: for a large random effects variance the effective degrees of freedom will be close to the number of levels of the grouping structure and for a very small random effects variance it will tend towards zero.

new methods omitted:

  • RLRsim (restricted likelihood tests for random effects via simulation — R package)
Bibliography
1. Bretagnolle, V. and Certain, G. and Houte, S. and Metais, M. (2004) Distribution maps and minimum abundance estimates for wintering auks in the Bay of Biscay, based on aerial surveys, Aquatic Living Resources 17:353-360
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