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. 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). 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. 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

alpha

Variational estimates of posterior inclusion probabilities for each hyperparameter setting.

mu

Variational estimates of posterior mean coefficients for each hyperparameter setting.

s

Variational 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.

varbvs