Description Usage Arguments Value References See Also Examples
This function fits robust Bayesian LMMs to data via robust REML estimating functions. The latters are those proposed by Richardson & Welsh (1995), which are robustified versions of restricted maximum likelihood (REML) estimating equations. Posterior sampling is done with an ABC-MCMC algorithm, where the data are summarised through a rescaled version of the aforementioned estimating functions; see Ruli et al. (2017) for the properties and details of the method. The current package version (0.1.2) supports only models with a single random effects. Extensions to more general settings will be provided in the future versions of the package.
1 2 |
nabc |
number of posterior samples. |
h.obj |
list of objects as returned by the |
chain.control |
parameters that control the tracing and the thinning of the chain(s). |
n.cores |
number of cores for parallel computation on non Windows machines. For |
list or list of lists with elements abc
and effi
. In case of n.cores
=1, effi
is the actual acceptance rate of the ABC-MCMC algorithm whereas in abc
are stored the posterior samples. The latters are stored as a (q + c) \timesnabc matrix, where q is the number of fixed effects, i.e. the number of columns in the design matrix and c = 2 is the number of variance components. Hence, the first q rows of the matrix abc
give the posterior samples for the fixed effects and the last two rows give the posterior samples for the log-variances of the fixed effects and the residual term, respectively. If n.cores
> 1, i.e. if simulations are performed in parallel, then a list of lists is returned, where each element of the list is a list with elements abc
and effi
, where abc
and effi
are as those aforementioned.
Ruli E., Sartori N. & Ventura L. (2017) Robust approximate Bayesian inference with an application to linear mixed models. https://arxiv.org/abs/1706.01752
Richardson A. M. & Welsh A. H. (1995) Robust restricted maximum likelihood in mixed linear models. Biometrics 51, 1429-1439.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | ## The following example is meant for function documentation.
## For realistic use probably you'll need to take a larger sample and choose a
## "better" bandwidth h.
data(ergoStool)
require(lme4)
fm1 <- lmer(effort~Type + (1| Subject), data = ergoStool)
## tune h to get 0.8% acceptance
hopt <- tune.h(effort~Type + (1|Subject), data = ergoStool, n.samp = 1e+4,
acc.rate = 0.01, n.sim.HJ = 100, grid.h = seq(0.3, 0.7, len = 3),
prior = list(beta.sd = 10, s2.scale = 5), n.cores = 1)
## draw posterior samples with hopt.
abc.tmp <- rblme(nabc = 1e+4, h.obj = hopt,
n.cores = 1)
# process ABC samples
abc.sim <- t(abc.tmp$abc)
abc.sim[,c(5,6)] <- exp(abc.sim[,c(5,6)])
# ABC posterior
colMeans(abc.sim)
# REML estimates
summary(fm1)
|
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