tune.h: Tune ABC distance bandwidth
In robustBLME: Robust Bayesian Linear Mixed-Effects Models using ABC

Description Usage Arguments Details Value References See Also

Tunes the bandwidth h of the ABC distance to get the desired level of acceptance rate specified via acc.rate. Besides tuning h, the function also builds the relevant quantities needed for running rblme. For generating such quantities an internal call to lmer is performed.

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tune.h(formula, data, ..., n.samp = 1e+5, n.sim.HJ = 500, acc.rate, grid.h, prior,
       cHub = 1.345, cHub2 = 2.07,
       init, n.cores = 1, use.h)

`formula`	two-sided linear formula object describing the fixed-effects part of the model, with the response on the left of a `~` operator and the terms, separated by `+` operators on the right. The `"\|"` character separates an expression for a model matrix and a grouping factor.
`data`	optional data frame containing the variables named in `formula`. By default the variables are taken from the environment of `lmer` called internally.
`...`	other arguments to be passed to `lmer`. Currently none is used.
`n.samp`	number of pilot posterior samples to be drawn with ABC for each value of `grid.h`.
`n.sim.HJ`	number of simulations to be used for computing the sensitivity and variability matrices.
`acc.rate`	desired acceptance rate of the ABC-MCMC algorithm.
`grid.h`	grid of h values within which the "optimal" value is to be found.
`prior`	named list of user-defined prior hyper-parameters. See "Details" below.
`cHub`	tuning constant of the Huber function for the location parameter.
`cHub2`	tuning constant of the Huber proposal 2 function for the scale parameter.
`init`	optional object to use for starting values. Currently ignored as initial values are taken from `lmer`.
`n.cores`	number of cores for parallel computation on non Windows machines.
`use.h`	bandwidth to be used for the ABC distance. If provided, no tuning for h is performed and `acc.rate` is ignored.

Given a specification of the formula and data the function calls internally rlmer and extracts from the resulting object all the necessary quantities. Then proceeds by finding the solution of the REML II robust estimating equations (Richardson & Welsh 1995), with the REML estimate used as starting point. The sensitivity and the variability matrices are computed by simulation at the solution of the robust REML II estimating equation. Depending on whether use.h or acc.rate and grid.h are specified, the function has a different behaviour. If acc.rate and grid.h are provided, then an adaptive step is performed in order to get an "optimal" h which gives the desired acceptance rate acc.rate. IN particular, for each value of grid.h, the function draws n.samp posterior samples with the ABC-MCMC algorithm and saves the resulting acceptance rate. Lastly, a function is built via a smoothing spline with acceptance rates being the xs and grid.h being the ys. The "optimal" value of h is found, within grid.h, as the prediction the spline function at acc.rate. If you already have an h value in mind then specify it via use.h and leave grid.h and acc.rate unspecified. Note that, in this case the acceptance rate of the ABC-MCMC algorithm may not be the one you wish to obtain since it depends in some complicated way also from use.h. Currently, the prior for the q fixed effects is the product of q scalar normals with mean zero and user-specified variance beta.sd (see Examples) equal for all the parameters. For the variance components the prior is a halfCauchy with user-specified scale s2.scale. Both variance parameters are assumed to have equal prior scale.

list.

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.

rblme, ergoStool.

robustBLME documentation built on May 1, 2019, 6:34 p.m.