impute {cglasso}

Imputation of Missing and Censored Values

Description

Imputes multivariate missing and censored values.

Usage

impute(object, type = c("mar", "censored", "both"), lambda.new, rho.new)

Arguments

object

an R object inheriting class ‘cglasso’, that is, the output of the model-fitting functions cglasso and cggm.

type

a description of the imputation required (see section ‘Description’). By default only the missing-at-random values are imputed.

lambda.new

value of the tuning parameter \lambda at which the imputations are required.

rho.new

value of the tuning parameter \rho at which the imputations are required.

Details

The impute function returns the response matrix with the imputed missing-at-random values (‘type = "mar"’), the imputed censored values (‘type = "censored"’), or both (‘type = "both"’).

If ‘type = "mar"’ then, for each row, the missing response values are replaced with the expected values of a multivariate normal distribution conditioned on the observed response values.

If ‘type = "censored"’ then, for each row, the censored response values are imputed using the expected values of a multivariate truncated normal distribution conditioned on the observed response values.

If ‘type = "both"’ then missing-at-random and censored values are imputed. In this case the returned matrix corresponds to the working response matrix computed during the E-Step.

Value

The impute function returns a response matrix with the required imputed data.

Author(s)

Luigi Augugliaro ([e-mail])

See Also

Model-fitting functions cglasso, cggm and the accessor functions coef.cglasso, fitted.cglasso, residuals.cglasso and predict.cglasso.

Examples

set.seed(123)
# Y ~ N(0, Sigma) and 
# 1. probability of left/right censored values equal to 0.05
# 2. probability of missing-at-random values equal to 0.05
n <- 100L
p <- 3L
rho <- 0.3
Sigma <- outer(1L:p, 1L:p, function(i, j) rho^abs(i - j))
Z <- rcggm(n = n, Sigma = Sigma, probl = 0.05, probr = 0.05, probna = 0.05)

out <- cglasso(. ~ ., data = Z)
rho.new <- mean(out$rho)

# imputing missing values
Y.impute <- impute(out, type = "mar", rho.new = rho.new)

# imputing censored values
Y.impute <- impute(out, type = "censored", rho.new = rho.new)

# imputing missing and censored values
Y.impute <- impute(out, type = "both", rho.new = rho.new)


# Y ~ N(XB, Sigma) and 
# 1. probability of left/right censored values equal to 0.05
# 2. probability of missing-at-random values equal to 0.05
n <- 100L
p <- 3L
q <- 2
b0 <- runif(p)
B <- matrix(runif(q * p), nrow = q, ncol = p)
X <- matrix(rnorm(n * q), nrow = n, ncol = q)
rho <- 0.3
Sigma <- outer(1L:p, 1L:p, function(i, j) rho^abs(i - j))
Z <- rcggm(n = n, b0 = b0, X = X, B = B, Sigma = Sigma, probl = 0.05, probr = 0.05, 
           probna = 0.05)

out <- cglasso(. ~ ., data = Z)
lambda.new <- mean(out$lambda)
rho.new <- mean(out$rho)

# imputing missing values
Y.impute <- impute(out, type = "mar", lambda.new = lambda.new, rho.new = rho.new)

# imputing censored values
Y.impute <- impute(out, type = "censored", lambda.new = lambda.new, rho.new = rho.new)

# imputing missing and censored values
Y.impute <- impute(out, type = "both", lambda.new = lambda.new, rho.new = rho.new)