Varying-Coefficient Mixture-of-Experts Models

VCMoE is an R package for fitting varying-coefficient mixture-of-experts models. It supports Gaussian, Binomial, and Negative-Binomial responses, with local-linear estimation, component label alignment, bandwidth selection, diagnostics, confidence bands, bootstrap inference, and generalized likelihood-ratio tests.

Version 0.2.0 provides two fitting engines. The default engine = "local_grid_em" preserves the original behavior, while engine = "joint_path_em" updates one observation-level responsibility path across all grid points. Joint-path fits use the same prediction, diagnostics, confidence-band, bootstrap, GLRT, and bandwidth-selection interfaces.

The package is intended for problems where component-specific response relationships and component probabilities change along a continuous coordinate, such as time, pseudotime, dose, or spatial location.

Installation

Install the released version from CRAN:

install.packages("VCMoE")

Install the development version from GitHub:

install.packages("remotes")
remotes::install_github("qc-zhao/VCMoE")

Load the package:

library(VCMoE)

Need help with installation or usage? Please open a GitHub issue:

https://github.com/qc-zhao/VCMoE/issues

Quick Start

set.seed(1)
sim <- simulate_vcmoe_gaussian(
  n = 300,
  k = 2,
  scenario = "well_separated"
)
fit <- vcmoe_fit(
  y ~ z1 | x1,
  data = sim$data,
  u = sim$data$u,
  k = 2,
  family = "gaussian",
  bandwidth = 0.25
)
coef(fit, "expert")
predict(fit, type = "posterior")
plot_coefficients(fit)

Select joint-path EM explicitly when one responsibility path should be shared across the local coefficient models:

joint_fit <- vcmoe_fit(
  y ~ z1 | x1,
  data = sim$data,
  u = sim$data$u,
  k = 2,
  family = "gaussian",
  bandwidth = 0.25,
  engine = "joint_path_em"
)

Joint-path runtime grows with the number of observations, grid points, and EM iterations. Dense grids are rejected by default; override the guard only after estimating the computational cost. Its nearest-grid sample log-likelihood trace is diagnostic and need not increase at every iteration; convergence is based on posterior and parameter deltas, which should always be inspected.

Joint-path analytic-style bands use an observed local-likelihood sandwich plug-in. They report score-imbalance diagnostics and do not model shared-path, label-selection, or finite-grid cross-grid responsibility uncertainty. Joint-path GLRT uses a paper-inspired sample-weighted grid-projected null and evaluates each observation once at its nearest grid point. This is a documented grid approximation, not an exact constrained MLE or exact manuscript criterion. vcmoe_glrt() therefore returns an uncalibrated statistic by default; analytic or bootstrap calibration must be requested explicitly. A failed or nonconverged null fit is never reported as valid inference.

Documentation

The full documentation website includes Gaussian, Binomial, and Negative-Binomial tutorials plus the function reference:

https://qc-zhao.github.io/VCMoE/

Useful links:

Citation

Please cite:

Zhao Q, Greenwood CMT, Zhang Q. Varying-Coefficient Mixture of Experts Model. arXiv:2601.01699. https://arxiv.org/abs/2601.01699