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Coefficient-specific GLRT for VCMoE coefficient variation

vcmoe_glrt.Rd

Fits a constrained null under the same local objective and computes a generalized likelihood-ratio statistic against the supplied VCMoE fit.

Usage

vcmoe_glrt(
  fit,
  data,
  test = c("coefficient", "constant_all"),
  coefficient_set = c("expert", "gating", "sigma", "theta"),
  component = NULL,
  term = NULL,
  calibration = c("analytic_epanechnikov", "bootstrap", "both", "none",
    "parametric_bootstrap"),
  B = 200L,
  seed = NULL,
  control = list(),
  refit_control = list(),
  verbose = FALSE
)

Arguments

fit

A vcmoe fit.

data

Original data frame used to fit fit.

test

Test type. "coefficient" tests one coefficient function; "constant_all" tests all fitted coefficient functions jointly.

coefficient_set

Coefficient block for coefficient-specific tests.

component

Component label or index for coefficient-specific tests.

term

Term name for coefficient-specific tests.

calibration

Calibration method. "analytic_epanechnikov" uses the Epanechnikov modified chi-square calibration; "bootstrap" uses parametric bootstrap calibration; "both" reports both. "parametric_bootstrap" is accepted as a backwards-compatible alias for "bootstrap".

B

Number of bootstrap calibration replicates.

seed

Optional random seed.

control

Controls for the constrained null optimizer.

refit_control

Controls overriding bootstrap full-model refits.

verbose

Whether to message progress.

Value

A vcmoe_glrt object with the observed lambda, analytic statistic, null fit, optional bootstrap replicate summary, and calibrated p-value when available.

Details

The primary path is coefficient-specific. The selected coefficient function is constrained to be constant in u: its local-linear slope is fixed to zero and its intercept is shared across grid points. The null is re-optimized rather than obtained by post-hoc averaging.

Analytic Epanechnikov calibration requires Epanechnikov density weights, scaled local-linear basis, and unit-scaled u. It reports lambda = ell_full - ell_null, analytic_statistic = rK * lambda, and a modified chi-square analytic_p_value. The diagnostic lrt_statistic = 2 * lambda is reported separately and is not used for the analytic p-value. Ridge penalties may be used to stabilize fitting but are excluded from the GLRT likelihood ratio.

vcmoe_glrt() supports fitted k = 2:10 models for both coefficient-specific and "constant_all" nulls. For k > 2, gating coefficient tests use identifiable baseline contrasts, e.g. component3_vs_component1. Reported p-values should be interpreted together with fit convergence, label ambiguity, component proportion, and null-optimizer diagnostics.