Compute the mean and variance of the coefficients, and the
posterior inclusion probabilities (PIPs), ignoring correlations between
variables. This is useful for inspecting or visualizing groups of
correlated variables (e.g., genetic markers in linkage disequilibrium).

varbvsindep (fit, X, Z, y)

## Arguments

fit |
Output of function `varbvs` . |

X |
n x p input matrix, where n is the number of samples,
and p is the number of variables. X cannot be sparse,
and cannot have any missing values (NA). |

Z |
n x m covariate data matrix, where m is the number of
covariates. Do not supply an intercept as a covariate
(i.e., a column of ones), because an intercept is
automatically included in the regression model. For no
covariates, set `Z = NULL` . |

y |
Vector of length n containing observations of binary
(`family = "binomial"` ) or continuous (```
family =
"gaussian"
``` ) outcome. For a binary outcome, all entries
of y must be 0 or 1. |

## Details

For the ith hyperparameter setting, `alpha[,i]`

is the
variational estimate of the posterior inclusion probability (PIP) for
each variable; `mu[,i]`

is the variational estimate of the
posterior mean coefficient given that it is included in the model; and
`s[,i]`

is the estimated posterior variance of the coefficient
given that it is included in the model.

## Value

alphaVariational estimates of posterior inclusion
probabilities for each hyperparameter setting.

muVariational estimates of posterior mean coefficients for
each hyperparameter setting.

sVariational estimates of posterior variances for each
hyperparameter setting.

## References

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 also

`varbvs`