[R-sig-ME] WAIC calculation in MCMCglmm

[Jed Macdonald]

Dear list,

I’ve fitted a series of univariate mixed models of varying complexity in
the 'MCMCglmm' package, and would like to compute WAIC for model selection
purposes, for comparison with DIC, and with AICc returned for equivalent
models fitted in 'lme4'. As I understand it, a first step in the WAIC
calculation is to compute the log pointwise predictive density (i.e.
pointwise log-likelihood), which is evaluated using draws from the retained
posterior simulations (after burn-in). For the number of data points *N*
and number of retained draws *S*, we can then get a *N* x *S*
log-likelihood matrix, which can be used to estimate pointwise
out-of-sample prediction accuracy (e.g. using WAIC or LOO cross-validation
in the ‘loo’ package) (see Gelman et al. 2014, Vehtari et al. 2016 for an
overview).

MCMCglmm doesn’t return the pointwise log-likelihood directly, so my
thinking was to use the deviance (D), given by D = −2log-likelihood in
MCMCglmm, which is returned for each chain iteration. My question(s) is, do
these values reflect the mean deviance across all *N* data points for a
given iteration? And if so, is there a way to decompose this to pointwise
deviance (and hence pointwise log-likelihood) values in an MCMCglmm model?

Any advice would much appreciated!

Best regards,
Jed

Gelman, A., Hwand, J. and Vehtari, A. (2014) Understanding predictive
information criteria for Bayesian models. Stat Comput 24, 997-1016.
Vehtari, A., Gelman, A. and Gabry, J. (2016) Practical Bayesian model
evaluation using leave-one-out cross-validation and WAIC. arXiv:1507.04544.



-- 
Jed Macdonald
PhD candidate
MARICE
Faculty of Life and Environmental Sciences
University of Iceland
(currently visiting the School of BioSciences, The University of Melbourne)
e: jedimacdonald at gmail.com
t: +61 428 242 066

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