# Imputation of Missing and Censored Values Imputes multivariate missing and censored values. ```r impute(object, type = c("mar", "censored", "both"), lambda.new, rho.new) ``` ## Arguments - `object`: an 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. ## Returns The `impute` function returns a response matrix with the required imputed data. ## Author(s) Luigi Augugliaro (luigi.augugliaro@unipa.it ) ## See Also Model-fitting functions `cglasso`, `cggm` and the accessor functions `coef.cglasso`, `fitted.cglasso`, `residuals.cglasso` and `predict.cglasso`. ## Examples ```r 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) ```

impute function