spikeAndSlab: Set up and sample a spike-and-slab prior model.
In fabian-s/spikeSlabGAM: Bayesian Variable Selection and Model Choice for Generalized Additive Mixed Models
spikeAndSlab R Documentation
Set up and sample a spike-and-slab prior model.
Description
This function sets up a spike-and-slab model for variable selection and model
choice in generalized additive models and samples its posterior. It uses a
blockwise Metropolis-within-Gibbs sampler and the redundant multiplicative
parameter expansion described in the reference. This routine is not meant to
be called directly by the user – spikeSlabGAM provides a
formula-based interface for specifying models and takes care of (most of) the
housekeeping. Sampling of the chains is done in parallel using package
parallel. A "SOCK" cluster is set up under Windows to do so (and
closed after computations are done, I try to clean up after myself), see
makeCluster etc. Use options(mc.cores =<foo>)
to set the (maximal) number of processes forked by the parallelization. If
options()$mc.cores is unspecified, it is set to 2.
Usage
spikeAndSlab(
y,
X,
family = c("gaussian", "binomial", "poisson"),
hyperparameters = list(),
model = list(),
mcmc = list(),
start = list()
)
Arguments
y
response
X
design matrix
family
(character) the family of the response, defaults to
normal/Gaussian response
hyperparameters
a list of hyperparameters controlling the priors (see
details)
model
a list with information about the grouping structure of the
model (see details)
mcmc
(optional) list setting arguments for the sampler (see details)
start
(optional) list containing the starting values for \beta,
\gamma, \tau^2, \sigma^2, w and, optionally, the random seed
Details
Details for model specification:
hyperparameters-
whyperparameters for the Beta-prior for w;
defaults to c(alphaW = 1, betaW = 1), i.e. a uniform distribution.
tau2hyperparameters for the \Gamma^{-1}-prior of the
hypervariances \tau^2; defaults to c(a1 = 5, a2 = 25)
gammasets v_0, the ratio between the spike and slab
variances, defaults to c(v0 = 0.00025)
sigma2hyperparameters for \Gamma^{-1}-prior for error
variance; defaults to c(b1 = 1e-4, b2 = 1e-4). Only relevant for Gaussian
response.
varKsivariance for prior of \xi, defaults to
1
ksiDFdefaults to 0 for a gaussian prior for \xi, else
induces a t-prior for \xi
with ksiDF degrees of freedom.
model-
groupIndicatorsa factor that maps the columns of X to the
different model terms
Ha matrix containing the hierarchy of
the penalized model terms
nnumber of observations
qlength of \beta
scalescale/weights of
the response, defaults to rep(1, n), use this to specify number of
trials for binomial data
offsetdefaults to rep(0,
n)
mcmc-
nChainshow many parallel chains to run: defaults to 3
chainLengthhow many samples should be generated per chain,
defaults to 500
burninhow many initial iterations should be
discarded, defaults to 100
thinsave only every thin-th
iteration, defaults to 5
verboseverbose output and report
progress? defaults to TRUE
returnSamplesdefaults to TRUE
sampleYgenerate samples of y and its conditional expectation
from posterior predictive? defaults to FALSE
useRandomStartuse random draw or ridge estimate for beta as
starting value? defaults to TRUE, i.e. random starting values.
blocksizeapprox. blocksizes of the updates for \alpha,
\xi. Defaults to 50 for gaussian responses and 5/15 for non-gaussian
responses.
scalemodehow to do term-wise rescaling of
subvectors of \xi in each iteration: 0 means no rescaling, 1 means
rescaling s.t. each mean(|\xi_g|) = 1, 2 means rescaling s.t. each
max(|\xi_g|) = 1
modeSwitchingprobability to do P-IWLS
with the mode of the proposal set to the current value, which is useful if
the chain gets stuck. Defaults to 0.05. Increase this if acceptance rates
are too low.
reduceRetdon't return data and samples for
\alpha, \xi, \tau^2? defaults to FALSE
start
betastarting
values for \beta. Defaults to a modified approximate ridge-penalized ML
estimate. See vignette for details on default specification.
gammastarting values for \gamma. Defaults to a vector of
1's if mcmc$useRandomStart is FALSE, otherwise drawn from the
prior.
tau2starting values for \tau^2. Defaults to the
mode of the prior if mcmc$useRandomStart is FALSE, otherwise
drawn from the prior.
sigma2starting values for
\sigma^2. Only relevant for Gaussian response. Defaults to the variance
of the response divided by the number of covariates if
mcmc$useRandomStart is FALSE, otherwise drawn from the prior.
wstarting value for w. Defaults to the mean of the prior
if mcmc$useRandomStart is FALSE, otherwise drawn from the
prior.
seedSets RNG seed for reproducible results. Parallel
chains are seeded with this seed incremented by the number of the chain.
Value
a list with components:
formulasee
arguments
datasee arguments
familysee
arguments
ysee arguments
Xsee arguments
hyperparameterssee arguments
modelsee
arguments
mcmcsee arguments
startsee
arguments
posteriorPreda list with entries mu and
y containing samples of the expected values and realizations of the
response from the posterior predictive
postMeansa list
containing the posterior means of the parameters:
betathe regression coefficients
alphaksitauhypervariances of the penalized model
terms
gammainclusion indicator variables of the model
terms
pV1P(\gamma = 1)
whyperparameter
for gamma
sigma2error variance (for Gaussian data)
logLiklog likelihood
logPostlog of
(unnormalized) posterior
samplesa list containing the
posterior samples of the parameters, see above for explanation of the
entries
DICa vector with DIC, pD, \bar{D},\hat{D}.
Usually doesn't make much sense for this kind of model because of the
posterior's multimodality.
fitteda matrix with the
posterior mean of the linear predictor in the first column and the
posterior mean of the expected response in the second.
runTimeof the sampler, in seconds
Author(s)
Fabian Scheipl, Daniel Sabanes Bove
References
Scheipl, F. (2010) Normal-Mixture-of-Inverse-Gamma Priors for
Bayesian Regularization and Model Selection in Structured Additive
Regression Models. LMU Munich, Department of Statistics: Technical
Reports, No.84 (https://epub.ub.uni-muenchen.de/11785/)
fabian-s/spikeSlabGAM documentation built on Oct. 27, 2024, 11:47 a.m.
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| spikeAndSlab | R Documentation |
Set up and sample a spike-and-slab prior model.
Description
This function sets up a spike-and-slab model for variable selection and model
choice in generalized additive models and samples its posterior. It uses a
blockwise Metropolis-within-Gibbs sampler and the redundant multiplicative
parameter expansion described in the reference. This routine is not meant to
be called directly by the user – spikeSlabGAM provides a
formula-based interface for specifying models and takes care of (most of) the
housekeeping. Sampling of the chains is done in parallel using package
parallel. A "SOCK" cluster is set up under Windows to do so (and
closed after computations are done, I try to clean up after myself), see
makeCluster etc. Use options(mc.cores =<foo>)
to set the (maximal) number of processes forked by the parallelization. If
options()$mc.cores is unspecified, it is set to 2.
Usage
spikeAndSlab(
y,
X,
family = c("gaussian", "binomial", "poisson"),
hyperparameters = list(),
model = list(),
mcmc = list(),
start = list()
)
Arguments
y |
response |
X |
design matrix |
family |
(character) the family of the response, defaults to normal/Gaussian response |
hyperparameters |
a list of hyperparameters controlling the priors (see details) |
model |
a list with information about the grouping structure of the model (see details) |
mcmc |
(optional) list setting arguments for the sampler (see details) |
start |
(optional) list containing the starting values for |
Details
Details for model specification:
hyperparameters-
whyperparameters for the
Beta-prior forw; defaults toc(alphaW = 1, betaW = 1), i.e. a uniform distribution.tau2hyperparameters for the
\Gamma^{-1}-prior of the hypervariances\tau^2; defaults toc(a1 = 5, a2 = 25)gammasets
v_0, the ratio between the spike and slab variances, defaults toc(v0 = 0.00025)sigma2hyperparameters for
\Gamma^{-1}-prior for error variance; defaults toc(b1 = 1e-4, b2 = 1e-4). Only relevant for Gaussian response.varKsivariance for prior of
\xi, defaults to 1ksiDFdefaults to 0 for a gaussian prior for
\xi, else induces a t-prior for\xi
with
ksiDFdegrees of freedom. model-
groupIndicatorsa factor that maps the columns of X to the different model terms
Ha matrix containing the hierarchy of the penalized model terms
nnumber of observations
qlength of
\betascalescale/weights of the response, defaults to
rep(1, n), use this to specify number of trials for binomial dataoffsetdefaults to
rep(0, n)
mcmc-
nChainshow many parallel chains to run: defaults to 3
chainLengthhow many samples should be generated per chain, defaults to 500
burninhow many initial iterations should be discarded, defaults to 100
thinsave only every
thin-th iteration, defaults to 5verboseverbose output and report progress? defaults to TRUE
returnSamplesdefaults to TRUE
sampleYgenerate samples of y and its conditional expectation from posterior predictive? defaults to FALSE
useRandomStartuse random draw or ridge estimate for beta as starting value? defaults to TRUE, i.e. random starting values.
blocksizeapprox. blocksizes of the updates for
\alpha, \xi. Defaults to 50 for gaussian responses and 5/15 for non-gaussian responses.scalemodehow to do term-wise rescaling of subvectors of
\xiin each iteration: 0 means no rescaling, 1 means rescaling s.t. each mean(|\xi_g|) = 1, 2 means rescaling s.t. each max(|\xi_g|) = 1modeSwitchingprobability to do P-IWLS with the mode of the proposal set to the current value, which is useful if the chain gets stuck. Defaults to
0.05. Increase this if acceptance rates are too low.reduceRetdon't return data and samples for
\alpha, \xi, \tau^2? defaults to FALSE
startbetastarting values for
\beta. Defaults to a modified approximate ridge-penalized ML estimate. See vignette for details on default specification.gammastarting values for
\gamma. Defaults to a vector of 1's ifmcmc$useRandomStartisFALSE, otherwise drawn from the prior.tau2starting values for
\tau^2. Defaults to the mode of the prior ifmcmc$useRandomStartisFALSE, otherwise drawn from the prior.sigma2starting values for
\sigma^2. Only relevant for Gaussian response. Defaults to the variance of the response divided by the number of covariates ifmcmc$useRandomStartisFALSE, otherwise drawn from the prior.wstarting value for
w. Defaults to the mean of the prior ifmcmc$useRandomStartisFALSE, otherwise drawn from the prior.seedSets RNG seed for reproducible results. Parallel chains are seeded with this seed incremented by the number of the chain.
Value
a list with components:
formulasee arguments
datasee arguments
familysee arguments
ysee arguments
Xsee arguments
hyperparameterssee arguments
modelsee arguments
mcmcsee arguments
startsee arguments
posteriorPreda list with entries
muandycontaining samples of the expected values and realizations of the response from the posterior predictivepostMeansa list containing the posterior means of the parameters:
betathe regression coefficients
alphaksitauhypervariances of the penalized model terms
gammainclusion indicator variables of the model terms
pV1P(\gamma = 1)whyperparameter for
gammasigma2error variance (for Gaussian data)
logLiklog likelihood
logPostlog of (unnormalized) posterior
samplesa list containing the posterior samples of the parameters, see above for explanation of the entries
DICa vector with
DIC, pD, \bar{D},\hat{D}. Usually doesn't make much sense for this kind of model because of the posterior's multimodality.fitteda matrix with the posterior mean of the linear predictor in the first column and the posterior mean of the expected response in the second.
runTimeof the sampler, in seconds
Author(s)
Fabian Scheipl, Daniel Sabanes Bove
References
Scheipl, F. (2010) Normal-Mixture-of-Inverse-Gamma Priors for Bayesian Regularization and Model Selection in Structured Additive Regression Models. LMU Munich, Department of Statistics: Technical Reports, No.84 (https://epub.ub.uni-muenchen.de/11785/)
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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