coef.bas {BAS} | R Documentation

## 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

    ## 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
`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'
`...` | other optional arguments
`x` | object of class 'coef.bas' to print
`digits` | number of significant digits to print

### 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. The value reported for the intercept is under the centered parameterization. Under the Gaussian error model it will be centered at the sample mean of Y.

### Author(s)

Merlise Clyde clyde@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

### See Also

`bas`, `confint.coef.bas`

Other bas methods: `BAS`, `bas.lm`, `confint.coef.bas`, `confint.pred.bas`, `diagnostics`, `fitted.bas`, `force.heredity.bas`, `image.bas`, `predict.basglm`, `predict.bas`, `summary.bas`, `update.bas`, `variable.names.pred.bas`

### Examples

    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

[Package BAS version 1.5.3 Index]