Robust-Regression Combined-Likelihood Inference for KK Designs

Fits a single stacked robust regression over matched-pair differences and reservoir observations for KK matching-on-the-fly designs with continuous responses.

Details

Model. Analogous to InferenceContinKKOLSOneLik's single stacked design (matched-pair difference rows plus reservoir rows fit in one regression, treatment coefficient \(\beta_T\)), but fit with a robust M/MM-estimator (MASS::rlm, or an internal Rcpp IRLS kernel when use_rcpp = TRUE) instead of ordinary least squares. "MM" (the default method) starts from an LQS-based high-breakdown fit; "M" can warm-start from OLS (start_with_ols = TRUE).

Likelihood tier. likelihood_tier = "quasi": the robust objective is not a normalized likelihood, so only Wald-type asymptotic inference is available (compute_wald_confidence_interval()/ compute_wald_two_sided_pval(), aliased by the standard compute_asymp_* names) — no score/gradient/likelihood-ratio testing types, unlike the OLS one-likelihood sibling.

Assumptions. Continuous response; independent matched pairs and/or independent reservoir subjects; no censoring; a KK matching-on-the-fly design. Robust regression trades some efficiency under exactly-Gaussian errors for resistance to outliers and heavy tails.

References

Kapelner, A. and Krieger, A. M. (2014). Matching on-the-fly: Sequential allocation with higher power and efficiency. Biometrics, 70(2), 378-388. doi:10.1111/biom.12148 . (KK14 in REFERENCES.md.)

See also

InferenceContinKKRobustRegrIVWC for the inverse-variance-weighted-combination alternative to this one-likelihood combined-fit approach. Analogous Python API: statsmodels RLM.

Super class

Inference -> InferenceContinKKRobustRegrOneLik

Methods

Public methods

• InferenceContinKKRobustRegrOneLik$set_custom_randomization_statistic_function()

• InferenceContinKKRobustRegrOneLik$set_custom_randomization_statistic_cpp()

• InferenceContinKKRobustRegrOneLik$approximate_randomization_distribution_beta_hat_T()

• InferenceContinKKRobustRegrOneLik$supports_rand_pval_for_incidence()

• InferenceContinKKRobustRegrOneLik$compute_rand_two_sided_pval()

• InferenceContinKKRobustRegrOneLik$clone()

+ inherited public methods from Inference

• Inference$capabilities()
• Inference$compute_asymp_confidence_interval()
• Inference$compute_asymp_two_sided_pval()
• Inference$compute_estimate()
• Inference$compute_exact_confidence_interval()
• Inference$compute_exact_two_sided_pval_for_treatment_effect()
• Inference$duplicate()
• Inference$get_analysis_data()
• Inference$get_covariates()
• Inference$get_design_object()
• Inference$get_model_formula()
• Inference$get_nonestimable_reason()
• Inference$get_nonestimable_stage()
• Inference$get_optimization_alg()
• Inference$get_response()
• Inference$get_response_type()
• Inference$get_treatment()
• Inference$initialize()
• Inference$is_nonestimable()
• Inference$set_optimization_alg()
• Inference$set_seed()
• Inference$supports()

---

InferenceContinKKRobustRegrOneLik$set_custom_randomization_statistic_function()

Usage

InferenceContinKKRobustRegrOneLik$set_custom_randomization_statistic_function(
  custom_randomization_statistic_function
)

---

InferenceContinKKRobustRegrOneLik$set_custom_randomization_statistic_cpp()

Usage

InferenceContinKKRobustRegrOneLik$set_custom_randomization_statistic_cpp(fn)

---

InferenceContinKKRobustRegrOneLik$approximate_randomization_distribution_beta_hat_T()

Usage

InferenceContinKKRobustRegrOneLik$approximate_randomization_distribution_beta_hat_T(
  r = 501,
  delta = 0,
  transform_responses = "none",
  show_progress = TRUE,
  permutations = NULL,
  debug = FALSE,
  zero_one_logit_clamp = .Machine$double.eps
)

---

InferenceContinKKRobustRegrOneLik$supports_rand_pval_for_incidence()

Usage

InferenceContinKKRobustRegrOneLik$supports_rand_pval_for_incidence()

---

InferenceContinKKRobustRegrOneLik$compute_rand_two_sided_pval()

Usage

InferenceContinKKRobustRegrOneLik$compute_rand_two_sided_pval(
  r = 501,
  delta = 0,
  transform_responses = "none",
  na.rm = TRUE,
  show_progress = TRUE,
  permutations = NULL,
  zero_one_logit_clamp = .Machine$double.eps
)

---

InferenceContinKKRobustRegrOneLik$clone()

The objects of this class are cloneable with this method.

Usage

InferenceContinKKRobustRegrOneLik$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.