residuals {cglasso}

Extract Model Residuals

Description

Extracts model residuals from an R object inheriting class ‘cglasso’.

Usage

## S3 method for class 'cglasso'
residuals(object, type = c("observed", "working"), lambda.id, rho.id,
          drop = TRUE, ...)

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 desired residuals (see section ‘Details’).

lambda.id

a vector of integers used to specify the \lambda-values.

rho.id

a vector of integers used to specify the \rho-values.

drop

logical. Dimensions can only be dropped if their extent is one.

...

further arguments passed to or from other methods.

Details

The accessor function ‘residuals’ returns an array storing the ‘observed’ or ‘working’ residuals, depending on the argument type.

The ‘observed’ residuals are defined as the difference between the observed response values and the corresponding fitted expected values. For missing and censored response values, the ‘observed’ residuals are set equal to ‘NA’.

The ‘working’ residuals are obtained as a byproduct of the EM-algorithm used to fit the model. In the E-step, the algorithm computes the ‘working’ response matrix, that is, the response matrix with missing values replaced by the conditional expected values of the multivariate normal distribution and censored values replaced by the conditional expected values of the multivariate truncated normal distribution. The ‘working’ residuals are defined as the difference between ‘working’ responses and fitted expected values.

Value

The accessor function ‘residuals’ returns an array storing the desired residuals.

Author(s)

Luigi Augugliaro ([e-mail])

See Also

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

Examples

set.seed(123)
# Y ~ N(0, Sigma) and probability of left/right censored values equal to 0.05
n <- 1000L
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)
out <- cglasso(. ~ ., data = Z)
residuals(out, type = "observed", rho.id = 3L, drop = TRUE)
residuals(out, type = "working", rho.id = 3L, drop = TRUE)

# Y ~ N(b0 + XB, Sigma)  and probability of left/right censored values equal to 0.05
n <- 1000L
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)
out <- cglasso(. ~ ., data = Z)
residuals(out, type = "observed", lambda.id = 3L, rho.id = 3L, drop = TRUE)
residuals(out, type = "working", lambda.id = 3L, rho.id = 3L, drop = TRUE)