nmfre.inference: Statistical inference for the coefficient matrix C from...

In nmfkc: Non-Negative Matrix Factorization with Kernel Covariates

Statistical inference for the coefficient matrix C from NMF-RE

Description

nmfre.inference performs statistical inference on the coefficient matrix C (\Theta) from a fitted nmfre model, conditional on the estimated basis matrix \hat{X} and random effects \hat{U}.

Under the working model Y^* = Y - X\hat{U} \approx X C A + \varepsilon, inference is conducted via sandwich covariance estimation and one-step wild bootstrap with non-negative projection.

The result is compatible with nmfkc.DOT for visualization (pass the result directly as x with type = "YXA").

Usage

nmfre.inference(object, Y, A = NULL, wild.bootstrap = TRUE, ...)

Arguments

object	An object of class "nmfre" returned by nmfre.
Y	Observation matrix (P x N). Must match the data used in nmfre().
A	Covariate matrix (K x N). Default is NULL (intercept only).
wild.bootstrap	Logical. If TRUE (default), performs wild bootstrap for confidence intervals and bootstrap standard errors.
...	Additional arguments: wild.B Number of bootstrap replicates. Default is 500. wild.seed Seed for bootstrap. Default is 123. wild.level Confidence level for bootstrap CI. Default is 0.95. C.p.side P-value type: "one.sided" (default) or "two.sided". cov.ridge Ridge stabilization. Default is 1e-8. print.trace Logical. Default is FALSE.

Value

The input object with additional inference components:

sigma2.used	Estimated \sigma^2 used for inference.
C.vec.cov	Full covariance matrix for vec(C).
C.se	Sandwich standard errors for C.
C.se.boot	Bootstrap standard errors for C.
C.ci.lower	Lower CI bounds for C.
C.ci.upper	Upper CI bounds for C.
coefficients	Data frame with Basis, Covariate, Estimate, SE, BSE, z_value, p_value, CI_low, CI_high.
C.p.side	P-value type used.

References

Satoh, K. (2026). Wild Bootstrap Inference for Non-Negative Matrix Factorization with Random Effects. arXiv:2603.01468. https://arxiv.org/abs/2603.01468

See Also

nmfre, nmfkc.DOT, summary.nmfre

Examples

Y <- matrix(cars$dist, nrow = 1)
A <- rbind(intercept = 1, speed = cars$speed)
res <- nmfre(Y, A, rank = 1, wild.bootstrap = FALSE)
res2 <- nmfre.inference(res, Y, A)
res2$coefficients

nmfkc documentation built on July 14, 2026, 1:07 a.m.