Bauesian Spike-and-Slab Lasso Additive Model

Bauesian Spike-and-Slab Lasso Additive Model

bamlasso(
  x,
  y,
  family = c("gaussian", "binomial", "poisson", "cox"),
  offset = NULL,
  epsilon = 1e-04,
  maxit = 50,
  init = NULL,
  alpha = c(1, 0),
  ss = c(0.04, 0.5),
  b = 1,
  group = NULL,
  theta.weights = NULL,
  inter.hierarchy = NULL,
  inter.parents = NULL,
  Warning = FALSE,
  verbose = FALSE
)

Arguments

x

input matrix, of dimension nobs x nvars; each row is an observation vector.

y

response variable. Quantitative for family="gaussian", or family="poisson" (non-negative counts). For family="binomial", y should be either a factor with two levels, or a two-column matrix of counts or proportions (the second column is treated as the target class; for a factor, the last level in alphabetical order is the target class). For family="cox", y should be a two-column matrix with columns named 'time' and 'status'. The latter is a binary variable, with '1' indicating death, and '0' indicating right censored. The function Surv() in package survival produces such a matrix.

family

Response type (see above).

offset

A vector of length nobs that is included in the linear predictor.

epsilon

positive convergence tolerance e; the iterations converge when |dev - dev_old|/(|dev| + 0.1) < e.

maxit

integer giving the maximal number of EM iterations.

init

vector of initial values for all coefficients (not for intercept). If not given, it will be internally produced.

alpha

alpha=1: mixture double-exponential prior; alpha=0: mixture normal prior.

ss

a vector of two positive scale values (ss[1] < ss[2]) for the spike-and-slab mixture prior, leading to different shrinkage on different predictors and allowing for incorporation of group information.

b

group-specific inclusion probabilities follow beta(1,b). The tuning parameter b can be a vector of group-specific values.

group

a numeric vector, or an integer, or a list defining the groups of predictors. Only used for mde or mt priors. If group = NULL, all the predictors form a single group. If group = K, the predictors are evenly divided into groups each with K predictors. If group is a numberic vector, it defines groups as follows: Group 1: (group[1]+1):group[2], Group 2: (group[2]+1):group[3], Group 3: (group[3]+1):group[4], ..... If group is a list of variable names, group[[k]] includes variables in the k-th group.

theta.weights

Optional weights for the dispersion parameter.

inter.hierarchy

Optional specification for hierarchical interaction terms.

inter.parents

a numeric vector, or an integer, or a list defining the groups of predictors. If group = NULL, all the predictors form a single group. If group = K, the predictors are evenly divided into groups each with K predictors. If group is a numberic vector, it defines groups as follows: Group 1: (group[1]+1):group[2], Group 2: (group[2]+1):group[3], Group 3: (group[3]+1):group[4], ..... If group is a list of variable names, group[[k]] includes variables in the k-th group. The mixture prior is only used for grouped predictors. For ungrouped predictors, the prior is double-exponential or normal with scale ss[2] and mean 0.

Warning

logical. If TRUE, show the error messages of not convergence and identifiability.

verbose

logical. If TRUE, print out number of iterations and computational time.

Value

This function returns all outputs from the function glmnet, and some other values used in Bayesian hierarchical models.