compute_sufficient_stats: Compute one batch or node sufficient statistics for a normal...

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

Compute one batch or node sufficient statistics for a normal linear VCMM

Description

Computes the six-component summary that fully encodes one node's contribution to the normal linear VCMM likelihood. These statistics are additive across nodes and batches, so a central server can recover the full-data estimator by summing per-node summaries – without ever seeing the raw response or design matrices.

Usage

compute_sufficient_stats(y, X, Z, use_cpp = TRUE)

Arguments

y	Numeric response vector of length n.
X	Numeric n by p fixed-effects design matrix (intercept plus spline basis columns).
Z	Numeric n by q random-effects design matrix.
use_cpp	Logical. If TRUE (default), dispatch to the RcppArmadillo backend compute_sufficient_stats_cpp(). If FALSE, use the pure-R crossprod() reference path. The two paths agree to within floating-point summation order (typically below 1e-13 relative).

Details

The returned components are:

• a: sum(y^2), a scalar.

• b: crossprod(X, y), dimension p by 1.

• C: crossprod(X), dimension p by p.

• ZtZ: crossprod(Z), dimension q by q.

• Zty: crossprod(Z, y), dimension q by 1.

• XtZ: crossprod(X, Z), dimension p by q.

Since Day 16 the default backend is a RcppArmadillo implementation (use_cpp = TRUE). Pass use_cpp = FALSE to fall back to the pure-R reference path; this is used by the Day-16 bit-equivalence validation and is also useful for debugging.

Value

A list of class "vcmm_ss" with elements a, b, C, ZtZ, Zty, XtZ, and n_obs (the number of observations summarized).

References

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

See Also

Other sufficient statistics: accumulate_stats(), init_accumulator()

Examples

set.seed(1)
n <- 100; p <- 3; q <- 2
X <- cbind(1, matrix(rnorm(n * (p - 1)), n, p - 1))
Z <- matrix(rnorm(n * q), n, q)
y <- rnorm(n)

ss <- compute_sufficient_stats(y, X, Z)
str(ss)

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