vcov.cgaim {cgaim}

Calculate Variance-Covariance Matrix for a Fitted CGAIM Object

Description

Returns the variance covariance matrix of the main parameters of a fitted cgaim object. These parameters correspond to the index weights alpha and the scaling coefficients beta.

Usage

## S3 method for class 'cgaim'
vcov(object, parm = c("alpha", "beta"), type = c("normal",
  "bootstrap"), B = 100, complete = TRUE, ...)

## S3 method for class 'boot.cgaim'
vcov(object, parm = c("alpha", "beta"),
  complete = TRUE, ...)

Arguments

object

A cgaim or boot.cgaim object.

parm

The model components for which to get confidence intervals. Either "alpha" (the default) for index weights or "beta" for scaling coefficients.

type

The type of confidence intervals. Either "normal" (the default) or "bootstrap". See details.

B

The number of samples to be simulated.

complete

Indicates whether the full variance-covariance matrix should be returned when some of the parameters could not be estimated. If so, the matrix is padded with NAs.

...

Additional parameters to be passed to boot.cgaim for bootstrap replications.

Details

Two types of computation are currently implemented in the function. When type = "normal", variance-covariance matrices are computed assuming components are normally distributed. Beta coefficients are treated as regular linear regression coefficients and alpha coefficients are assumed to follow a Truncated Multivariate Normal distribution. The latter is obtained by simulating from TMVN (see tmvnorm) and computing the empirical variance covariance matrix from these simulations. The parameter B controls the number of simulations from the TMVN (and is not used when parm = "beta").

When type = "bootstrap", the variance-covariance matrix is computed on Bootstrap replications. In this case boot.cgaim is called internally and B corresponds to the number of replications. Alternatively, the user can directly call boot.cgaim and feed the result into vcov.boot.cgaim (see examples).

Value

A variance-covariance matrix object.

References

Masselot, P. and others, 2022. Constrained groupwise additive index models. Biostatistics.

Pya, N., Wood, S.N., 2015. Shape constrained additive models. Stat. Comput. 25, 543–559.

Wood, S.N., 2017. Generalized Additive Models: An Introduction with R, 2nd ed, Texts in Statistical Science. Chapman and Hall/CRC.

See Also

boot.cgaim for bootstrapping and confint.cgaim for confidence intervals.

Examples

# A simple CGAIM
n <- 200
x1 <- rnorm(n)
x2 <- x1 + rnorm(n)
z <- x1 + x2
y <- z + rnorm(n)
df1 <- data.frame(y, x1, x2) 
ans <- cgaim(y ~ g(x1, x2, acons = list(monotone = 1)), data = df1)

# (Truncated) Normal variance-covariance matrix
set.seed(1)
vcov(ans, B = 1000)
set.seed(1)
vcov(ans, parm = "alpha", B = 1000) # Same result
vcov(ans, parm = "beta", B = 1000)

# Confidence intervals by bootstrap (more computationally intensive, B should be increased)
set.seed(2)
vcov(ans, type = "boot", B = 10)

# Alternatively, bootstrap samples can be performed beforehand
set.seed(2) 
boot1 <- boot.cgaim(ans, B = 10)
vcov(boot1)