Generate a summary of the Bayesian variable selection model fitted using variational approximation methods.
# S3 method for varbvs summary(object, cred.int = 0.95, nv = 5, nr = 1000, …) # S3 method for summary.varbvs print(x, digits = 3, …)
| object | Output of function |
|---|---|
| cred.int | Size of credible interval (number between 0 and 1). |
| nv | Show detailed statistics for top nv variables, ranked according to their posterior inclusion probabilities. |
| nr | Number of Monte Carlo samples to draw to estimate credible intervals for coefficients of selected variables. |
| x | Output of function |
| digits | Number of digits shown when printing posterior probabilities of top nv variables. |
| ... | Additional print arguments. |
The printed summary is divided into three parts. The first part
summarizes the data and optimization settings. It also reports the
hyperparameter setting that yields the largest marginal
likelihood---more precisely, the approximate marginal likelihood
computed using the variational method. For the linear regression only
(family = "gaussian"), it reports the estimated proportion of
variance in the outcome explained by the model (PVE), and the credible
interval of the PVE estimate brackets. Note that this is the PVE in
the outcome after removing variance in the outcome due to linear
effects of the covariates.
The second part summarizes the approximate posterior distribution of
the hyperparameters (sigma, sa, logodds). The "estimate" column is the
value averaged over hyperparameter settings, treating objectlogw
as (unnormalized) log-marginal probabilities. The next column, labeled
"Pr>x", where x = cred.int gives the credible interval based on
these weights (computed using function cred).
The third part summarizes the variable selection results. This
includes the total number of variables included in the model at
different posterior probability thresholds, and a more detailed
summary of the variables included in the model with highest posterior
probability. For family = "gaussian", the "PVE" column gives
the estimated proportion of variance in the outcome explained by the
variable (conditioned on being included in the model). Again, this is
the PVE after removing variance in the outcome due to linear effects
of the covariates. Finally, note that the credible intervals reported
in the right-most column are Monte Carlo estimates, so the interval
will be slightly different each time summary is called; a
more accurate estimate can be obtained by setting input nr to a
larger number, at the cost of increased computation time.
An object of class summary.varbvs, to be printed by
print.summary.varbvs.
P. Carbonetto and M. Stephens (2012). Scalable variational inference for Bayesian variable selection in regression, and its accuracy in genetic association studies. Bayesian Analysis 7, 73--108.
# See help(varbvs) for examples.