vcov.vcmm_fit: Variance-covariance matrix of the fixed-effects from a vcmm...

In cevcmm: Communication-Efficient Varying Coefficient Mixed-Effects Models

Variance-covariance matrix of the fixed-effects from a vcmm fit

Description

Returns the asymptotic variance-covariance matrix of the fixed-effects coefficient vector \hat\beta from a fitted vcmm_fit. The matrix is computed as

\widehat{\mathrm{Var}}(\hat\beta) = \hat\sigma_\varepsilon^2 \cdot [K^{-1}]_{1:p,\, 1:p},

where K is the prior-augmented Hessian assembled at convergence and cached in object$K_inv. This is the standard plug-in asymptotic-normal variance estimator for the linear normal VCMM with fixed variance components.

Usage

## S3 method for class 'vcmm_fit'
vcov(object, which = c("beta", "alpha", "both"), ...)

Arguments

object	A vcmm_fit object.
which	Character: "beta" (default), "alpha", or "both".
...	Unused.

Details

Pass which = "alpha" for the random-effect block, which = "both" for the full (p+q) \times (p+q) joint matrix.

Value

A numeric matrix:

• "beta": p by p.

• "alpha": q by q.

• "both": (p+q) by (p+q), joint.

References

Jalili, L. and Lin, L.-H. (2025). Scalable and Communication-Efficient Varying Coefficient Mixed-Effects Models.

Examples

set.seed(1)
n <- 300
t <- runif(n); x <- runif(n)
Z <- matrix(rnorm(n * 3), n, 3)
y <- 2 + sin(2 * pi * t) * x +
     as.vector(Z %*% rnorm(3, sd = 0.5)) + rnorm(n, sd = 0.5)

fit <- vcmm(y, X = x, Z = Z, t = t,
            control = vcmm_control(sigma_eps = 0.5, sigma_alpha = 0.5))

V_beta <- vcov(fit)
dim(V_beta)

cevcmm documentation built on July 24, 2026, 5:07 p.m.