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Validation Evidence

This page answers, for each important model family, “how do I know this implementation actually computes what its documentation claims?” It is an index into the test suite (R/EDI/tests/testthat/), not a restatement of it — every row below names the specific test file(s) that check the corresponding fast_*/Inference* implementation against independent evidence, so a reader auditing correctness (or a maintainer touching a kernel) knows exactly which test to run or extend. All file paths are relative to R/EDI/tests/testthat/.

Four kinds of evidence appear throughout the suite, matching fix_documentation.md’s validation-evidence categories:

  1. Package-to-package comparisons — the coefficient/variance estimate from EDI’s own C++ kernel is checked against an independent R package’s implementation of the same model (stats::glm, survival::coxph, MASS::glm.nb, betareg::betareg, VGAM::vglm, ordinal::clm, lme4::glmer, glmmTMB, pscl::hurdle, geepack/multgee, copula, gamlss.dist) on the same simulated or real data, usually to a tight numerical tolerance.
  2. Closed-form/limiting-case reductions — a general kernel is checked against a simpler model it must mathematically reduce to in a special case (e.g. a frailty variance of zero, a single mixture component, an uncensored subset).
  3. Numerical-derivative checks — an analytic score/gradient/Hessian is checked against a finite-difference (numDeriv) approximation at the same parameter vector, independent of any reference package.
  4. Simulation/calibration checks — Monte Carlo simulation confirming an inference procedure’s operating characteristics (type-I error, coverage) are near their nominal targets, using SimulationFramework’s own built-in exact-binomial calibration test (see below), not just a single point comparison.

Continuous

EDI implementation Validated against Test file
fast_ols_with_var_cpp stats::lm test-rcpp-fitting-equivalence.R
fast_ols_with_var_cpp (real data) stats::lm on MASS::Boston test-rcpp-fitting-real-data.R
fast_robust_regression_cpp (M/MM) MASS::rlm test-rcpp-fitting-equivalence.R, test-rcpp-fitting-real-data.R (mtcars)
InferenceContinKKRobustRegrOneLik/IVWC (use_rcpp path) MASS::rlm fallback, and Rcpp-vs.-fallback bootstrap-weighted-estimate agreement test-kk-robust-regr-use-rcpp.R

Incidence / binary

EDI implementation Validated against Test file
fast_logistic_regression_with_var_cpp stats::glm(family=binomial) test-rcpp-fitting-equivalence.R, test-fast_glm_outputs.R
fast_probit_regression_with_var_cpp stats::glm(family=binomial(link="probit")) test-rcpp-fitting-equivalence.R; InferenceIncidProbitRegr vs. stats::glm in test-incidence-probit.R
fast_log_binomial_regression_with_var_cpp stats::glm(family=binomial(link="log")) test-rcpp-fitting-equivalence.R
fast_identity_binomial_regression_with_var_cpp stats::glm(family=binomial(link="identity")) test-rcpp-fitting-equivalence.R
Real-data check stats::glm on MASS::birthwt test-rcpp-fitting-real-data.R

Count

EDI implementation Validated against Test file
fast_poisson_regression_with_var_cpp stats::glm(family=poisson) test-rcpp-fitting-equivalence.R, test-poisson-delta-eta-step-halving.R (IRLS internals incl. step-halving)
fast_quasipoisson_regression_with_var_cpp stats::glm(family=quasipoisson) test-rcpp-fitting-equivalence.R
fast_neg_bin_with_var_cpp MASS::glm.nb test-rcpp-fitting-equivalence.R, test-negbin-gemv-gradient.R (fit + analytic-vs.-numerical gradient), test-negbin-weighted.R
fast_neg_bin_weighted_cpp MASS::glm.nb with case weights test-negbin-weighted.R
fast_truncated_negbin_count_cpp glmmTMB’s truncated_nbinom2 test-custom-implementation-canonical-reductions.R
fast_zinb_cpp glmmTMB zero-inflated NB test-rcpp-fitting-equivalence.R, real-data check on glmmTMB::Salamanders in test-rcpp-fitting-real-data.R
fast_zero_augmented_poisson_cpp (hurdle/ZIP) glmmTMB test-rcpp-fitting-equivalence.R, real-data check on glmmTMB::Salamanders
fast_hurdle_negbin_with_var_cpp pscl::hurdle(dist="negbin") test-rcpp-fitting-equivalence.R
Real-data check stats::glm(family=poisson)/MASS::glm.nb on MASS::quine test-rcpp-fitting-real-data.R
fast_cpoisson_combined_with_var_cpp (matched-pair + reservoir) reduces to canonical GLM fits in single-component cases test-custom-implementation-canonical-reductions.R

Ordinal

EDI implementation Validated against Test file
fast_ordinal_regression_with_var_cpp (proportional odds) ordinal::clm test-rcpp-fitting-equivalence.R; real-data check on ordinal::wine in test-rcpp-fitting-real-data.R
fast_ordinal_probit_regression_with_var_cpp ordinal::clm(link="probit") test-rcpp-fitting-equivalence.R
fast_ordinal_cloglog_regression_with_var_cpp ordinal::clm(link="cloglog") test-rcpp-fitting-equivalence.R
fast_ordinal_cauchit_regression_with_var_cpp ordinal::clm(link="cauchit") test-rcpp-fitting-equivalence.R
fast_adjacent_category_logit_with_var_cpp VGAM::vglm(family=acat) test-rcpp-fitting-equivalence.R
fast_continuation_ratio_regression_with_var_cpp VGAM::vglm(family=cratio) test-rcpp-fitting-equivalence.R
fast_stereotype_logit_with_var_cpp K=2 reduces to stats::glm(binomial); K=3 checked against score-at-MLE and finite-difference Hessian test-rcpp-fitting-equivalence.R
fast_ordinal_clmm/fast_ordinal_glmm_cpp buffer-reuse/equivalence checks test-ordinal-glmm-alpha-buf.R

Survival

EDI implementation Validated against Test file
fast_coxph_regression_cpp survival::coxph test-rcpp-fitting-equivalence.R; real-data check on survival::lung in test-rcpp-fitting-real-data.R; component-composition regression in test-cox-component-composition.R
fast_stratified_coxph_regression_cpp survival::coxph with strata() test-rcpp-fitting-equivalence.R
Cluster-robust Cox covariance survival::coxph’s cluster-robust vcov test-coxph-robust-vcov.R
fast_weibull_regression_general_cpp survival::survreg test-rcpp-fitting-equivalence.R, test-weibull-general-censoring.R; real-data check on survival::lung in test-rcpp-fitting-real-data.R
compute_weibull_rand_bootstrap_parallel_cpp reproduces survreg on the same bootstrap resamples test-brt-weibull-kernel-matches-reference.R
InferenceSurvivalKKWeibullMarginal survreg with cluster-robust / no-covariate fits test-weibull-marginal.R
Weibull frailty analytic score vs. numerical gradient; log-likelihood collapses to plain survreg Weibull log-likelihood as the frailty SD -> 0 test-weibull-frailty.R
fast_gehan_wilcox_stats/martingale-residual kernel survival::survdiff(rho=1); canonical Peto-Prentice weighted martingale residuals test-gehan-wilcox-fused-martingale.R; end-to-end InferenceSurvivalGehanWilcox check in the same file
fast_logrank_stats/martingale-residual kernel survival::survdiff; coxph martingale residuals test-logrank-fused-martingale.R
Log-rank/Gehan-Wilcoxon under general censoring consistency checks across censoring patterns test-logrank-gehan-wilcox-general-censoring.R
get_survival_stat_for_group/get_survival_stat_diff (KM median) canonical survfit median, including exact-crossing, tie, and non-estimable (returns NA, not Inf) edge cases test-km-median-canonical.R
KM/RMST under general censoring test-km-rmst-general-censoring.R
fast_dep_cens_transform_optim_cpp rho=0 score matches two independent lognormal survreg fits test-custom-implementation-canonical-reductions.R
fast_clayton_weibull_aft_optim_cpp singleton-only case matches plain survreg Weibull; pair score matches the copula package’s reference likelihood test-custom-implementation-canonical-reductions.R

Proportion

EDI implementation Validated against Test file
fast_beta_regression_with_var_cpp/fast_beta_regression_mle betareg::betareg test-rcpp-fitting-equivalence.R; real-data check on betareg::ReadingSkills in test-rcpp-fitting-real-data.R
fast_zero_one_inflated_beta_cpp factors into a betareg continuous submodel plus a nnet::multinom inflation submodel; likelihood matches gamlss.dist::dBEINF test-custom-implementation-canonical-reductions.R

GEE / GLMM (matched-design, correlated data)

EDI implementation Validated against Test file
KK GEE direct solver (binomial, Poisson) geepack test-kk-gee-parity.R
Ordinal KK GEE direct multgee backend fit test-kk-gee-parity.R
Incidence/count/proportion KK GEE R6 wrappers their own backend fits test-kk-gee-parity.R
fast_poisson_glmm_cpp lme4::glmer (Poisson, matched quadrature order) test-glmm-cpp-equivalence.R
fast_logistic_glmm_cpp lme4::glmer (binomial, matched quadrature order) test-glmm-cpp-equivalence.R
fast_hurdle_poisson_glmm_cpp glmmTMB’s truncated_poisson test-glmm-cpp-equivalence.R
fast_gaussian_lmm_cpp lme4::lmer fixed effects and variance components test-rcpp-fitting-equivalence.R
fast_clogit_plus_glmm_cpp (matched-pair + reservoir binary) dedicated equivalence suite test-clogit-plus-glmm-cpp-equivalence.R

Numerical/backend utilities

EDI implementation Validated against Test file
fast_log1pexp closed-form/limiting behavior, precision at extreme arguments test-fast-log1pexp.R
Bartlett likelihood-ratio approximation smoke-tested across families (InferenceCountPoisson, InferenceCountNegBin, InferenceContinKKOLSOneLik, InferenceSurvivalWeibullRegr, InferenceOrdinalPropOddsRegr, InferenceCountZeroInflatedNegBin/Poisson, InferenceCountHurdlePoisson) test-bartlett-lr-approx-smoke-families.R, test-bartlett-lr-plumbing.R, test-bartlett-lr-logit.R, test-bartlett-lr-ols-exact.R
Design-side BlockingStructure/ClusterStructure bootstrap-index generalization byte-identical (identical(), matched seeds) against each real class’s pre-generalization output test-design-blocking-structure-bootstrap-golden.R, test-design-cluster-structure-golden.R
Merged DesignFixedGreedyDOptimal behavior-preservation against the pre-merge DesignFixedAOptimal/DesignFixedDOptimal classes test-greedy-d-optimal-merged.R

Simulation/calibration checks

Point-estimate-vs-reference-package equivalence (above) confirms a single fit is numerically correct; it does not by itself confirm an inference procedure’s coverage or type-I error are correct, since a subtly wrong standard-error formula can still pass an equivalence test on the point estimate alone. SimulationFrameworkReport$summarize() closes that gap: for any (design, inference) pair it reports coverage_pval/size_pval — the exact two-sided binomial-test p-value of “true coverage = 1 - alpha” (respectively “true size = alpha”) over Nrep_W * Nrep_Y_w Monte Carlo replications — so a calibration claim is itself a hypothesis test with a controlled false-alarm rate, not an eyeballed point estimate (see vignette("reproducibility")’s “Monte Carlo error” section for why a single observed coverage rate near but not exactly at the nominal level is expected, and how many replications are enough to distinguish that from genuine miscalibration). Running SimulationFramework$new(...)$run() followed by SimulationFrameworkReport$new(sim)$summarize() for a given (design_classes_and_params, inference_classes_and_params, response_type) combination is the package’s built-in mechanism for producing this evidence for a specific method on demand; no single pre-computed report is checked into the repository as of this writing (unlike the point-estimate equivalence tests above, which run on every R CMD check).

Coverage note

This page indexes what the test suite already demonstrates; it is not a claim that every documented method has independent package-to-package validation evidence. Custom/composite estimators without an external single-package analogue (e.g. the matched-pair-plus-reservoir combined kernels, fast_cpoisson_combined_with_var_cpp and fast_clogit_plus_glmm_cpp) are instead validated by the closed-form-reduction and numerical-derivative methods described above, since no independent reference package implements the exact combined model to compare against directly.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.