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

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.

Value

A numeric matrix:

"beta": p by p.
"alpha": q by q.
"both": (p+q) by (p+q), joint.

Details

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

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)
#> [1] 11 11