coefficients.bma: Coefficients of a Bayesian Model Average object

Description

Extract conditional posterior means and standard deviations, marginal posterior means and standard deviations, posterior probabilities, and marginal inclusions probabilities under Bayesian Model Averaging from an object of class 'bas'

Usage

 ```1 2 3 4``` ```## S3 method for class 'bas' coef(object, n.models, estimator="BMA", ...) ## S3 method for class 'coef.bas' print(x, digits = max(3, getOption("digits") - 3),...) ```

Arguments

 `object` object of class 'bas' created by BAS `x` object of class 'coef.bas' to print `n.models` Number of top models to report in the printed summary, for coef the default is to use all models. To extract summaries for the Highest Probability Model, use n.models=1 or estimator="HPM". `estimator` return summaries for a selected model, rather than using BMA. Options are 'HPM' (highest posterior probability model) ,'MPM' (median probability model), and 'BMA' `digits` number of significant digits to print `...` other optional arguments

Details

Calculates posterior means and (approximate) standard deviations of the regression coefficients under Bayesian Model averaging using g-priors and mixtures of g-priors. Print returns overall summaries. For fully Bayesian methods that place a prior on g, the posterior standard deviations do not take into account full uncertainty regarding g. Will be updated in future releases.

Value

`coefficients` returns an object of class coef.bas with the following:

 `conditionalmeans` a matrix with conditional posterior means for each model `conditionalsd` standard deviations for each model `postmean` marginal posterior means of each regression coefficient using BMA `postsd` marginal posterior standard deviations using BMA `postne0` vector of posterior inclusion probabilities, marginal probability that a coefficient is non-zero

Note

With highly correlated variables, marginal summaries may not be representative of the joint distribution. Use `plot.coef.bas` to view distributions.

Author(s)

Merlise Clyde clyde@stat.duke.edu

References

Liang, F., Paulo, R., Molina, G., Clyde, M. and Berger, J.O. (2005) Mixtures of g-priors for Bayesian Variable Selection. Journal of the American Statistical Association. 103:410-423.
http://dx.doi.org/10.1198/016214507000001337

`bas`, `confint.coef.bas`

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```data("Hald") hald.gprior = bas.lm(Y~ ., data=Hald, n.models=2^4, alpha=13, prior="ZS-null", initprobs="Uniform", update=10) coef.hald.gprior = coefficients(hald.gprior) coef.hald.gprior plot(coef.hald.gprior) confint(coef.hald.gprior) #Estimation under Median Probability Model coef.hald.gprior = coefficients(hald.gprior, estimator="MPM") coef.hald.gprior plot(coef.hald.gprior) plot(confint(coef.hald.gprior)) coef.hald.gprior = coefficients(hald.gprior, estimator="HPM") coef.hald.gprior plot(coef.hald.gprior) confint(coef.hald.gprior) # To add estimation under Best Predictive Model ```

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