bas.lm {BAS} | R Documentation |
Sample without replacement from a posterior distribution on models
bas.lm(formula, data, n.models, alpha=NULL, prior="ZS", initprobs="Uniform", random=TRUE, update=NULL, bestmodel = NULL, bestmarg = NULL, prob.local = 0, user.prob=NULL)
formula |
linear model formula for the full model with all predictors, Y ~ X. All code assumes that an intercept will be included in each model. |
data |
data frame |
n.models |
number of models to sample |
initprobs |
vector of initial marginal inclusion
probabilities used for sampling without replacement or method,
if "Uniform" each predictor variable is equally likely to be
sampled (equivalent to random sampling without replacement). If
"eplogp", use the eplogprob function to aproximate the
Bayes factor to find initial marginal inclusion probabilitites and
sample without replacement the model probabilities using these
inclusion probabilaties. If "user", the user may specify a vector of
probabilities using the optional argument user.prob. This should
include the intercept with probability one. |
alpha |
optional hyperparameter in g-prior or hyper g-prior. For Zellner's g-prior, alpha = g, for the Liang et al hyper-g method, recommended choice is alpha = 3 or 4. |
prior |
prior distribution for regression coefficients. Choices include "AIC", "BIC", "g-prior", "ZS-null", "ZS-full", "hyper-g", "hyper-g-laplace", "EB-local", and "EB-global" |
random |
A logical variable indicating whether to use the stochastic (random=TRUE) or deterministic (random=FALSE) algorithm for sampling models without replacement |
update |
number of iterations between potential updates of the sampling probabilities. If NULL do not update, otherwise the algorithm will update using the marginal inclusion probabilities |
bestmodel |
optional binary vector representing a model to initialize the sampling. If NULL sampling starts with the Full model |
bestmarg |
optional value for the log marginal associated with the bestmodel |
prob.local |
An experimental option to allow sampling of models "near" the median probability model. Not recommended for use at this time |
user.prob |
User specified probabilities for sampling |
BAS provides two search algorithms to find high probability models for use in Bayesian Model Averaging or Bayesian model selection.
bas
returns an object of class BMA
An object of class BMA
is a list containing at least the following components:
postprob |
the posterior probabilities of the models selected |
namesx |
the names of the variables |
R2 |
R2 values for the models |
logmarg |
values of the log of the marginal likelihood for the models |
n.vars |
total number of independent variables in the full model, including the intercept |
size |
the number of independent variables in each of the models, includes the intercept |
which |
a list of lists with one list per model with variables that are included in the model |
probne0 |
the posterior probability that each variable is non-zero |
ols |
list of lists with one list per model giving the OLS estimate of each (nonzero) coefficient for each model |
ols.se |
list of lists with one list per model giving the OLS standard error of each coefficient for each model |
prior |
the name of the prior that created the BMA object |
alpha |
value of hyperparameter in prior used to create the BMA object. |
Y |
response |
X |
matrix of predictors |
The function summary.bma
, is used to print a summary of
the results. The function plot.bma
is used to plot
posterior distributions for the coefficients and
image.bma
provides an image of the distribution over models.
Posterior summaries of coefficients can be extracted using
coefficients.bma
. Fitted values and predictions can be
obtained using the functions fitted.bma
and predict.bma
.
BMA objects may be updated to use a different prior (without rerunning
the sampler) using the function update.bma
.
Uniform prior probabilities on models are the only option currently. A future update should allow alternative priors on models to be incorporated into the sampling and posterior inference. For now, users may manually reweight output using the log marginal likelihoods to update posterior model probabilities and probne0.
Merlise Clyde (clyde@stat.duke.edu) and Michael Littman
Clyde, M. Ghosh, J. and Littman, M. (2009) Bayesian Adaptive Sampling for Variable Selection. Department of Statistical Science Discussion Paper. Duke University.
Clyde, M. and George, E. I. (2004) Model Uncertainty. Statist. Sci.,
19, 81-94.
http://www.isds.duke.edu/~clyde/papers/statsci.pdf
Clyde, M. (1999) Bayesian Model Averaging and Model Search Strategies (with discussion). In Bayesian Statistics 6. J.M. Bernardo, A.P. Dawid, J.O. Berger, and A.F.M. Smith eds. Oxford University Press, pages 157-185.
Hoeting, J. A., Madigan, D., Raftery, A. E. and Volinsky, C. T. (1999)
Bayesian model averaging: a tutorial (with discussion). Statist. Sci.,
14, 382-401.
http://www.stat.washington.edu/www/research/online/hoeting1999.pdf
Liang, F., Paulo, R., Molina, G., Clyde, M. and Berger,
J.O. (2005) Mixtures of g-priors for Bayesian Variable
Selection.
http://www.stat.duke.edu/05-12.pdf
Zellner, A. (1986) On assessing prior distributions and Bayesian regression analysis with g-prior distributions. In Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti, pp. 233-243. North-Holland/Elsevier.
Zellner, A. and Siow, A. (1980) Posterior odds ratios for selected regression hypotheses. In Bayesian Statistics: Proceedings of the First International Meeting held in Valencia (Spain), pp. 585-603.
summary.bma
,
coefficients.bma
,
print.bma
,
predict.bma
,
fitted.bma
plot.bma
,
image.bma
,
eplogprob
,
update.bma
demo(BAS.hald) ## Not run: demo(BAS.USCrime)