Cumulative Cloglog Inference for Ordinal Responses

Complementary log-log cumulative-odds ordinal regression: \(P(Y \le k \mid w, x) = 1 - \exp\{-\exp(\alpha_k - \beta_T w - \beta_X^\top x)\}\), where \(\alpha_k\) are category-specific cutpoints and \(\beta_T\) is the treatment coefficient on the cloglog scale. Fit by maximum likelihood. The cloglog link is asymmetric (unlike logit/probit) and is the natural ordinal generalization of a proportional-hazards/grouped survival-time model, so it is preferred when the underlying process is plausibly a discretized time-to-event or extreme-value mechanism. likelihood_tier = "full": exposes likelihood-ratio, score, gradient, and parametric-likelihood-bootstrap inference in addition to Wald/asymptotic and Bayesian-bootstrap paths.

References

Agresti, A. (2010). Analysis of Ordinal Categorical Data (2nd ed.). Wiley. Ch. 3-4 (cumulative link models); McCullagh, P. (1980). "Regression Models for Ordinal Data." JRSS-B, 42(2), 109-142.

See also

https://en.wikipedia.org/wiki/Ordinal_regression

Super class

Inference -> InferenceOrdinalCloglogRegr

Methods

Public methods

• InferenceOrdinalCloglogRegr$set_custom_randomization_statistic_function()

• InferenceOrdinalCloglogRegr$set_custom_randomization_statistic_cpp()

• InferenceOrdinalCloglogRegr$approximate_randomization_distribution_beta_hat_T()

• InferenceOrdinalCloglogRegr$supports_rand_pval_for_incidence()

• InferenceOrdinalCloglogRegr$compute_rand_two_sided_pval()

• InferenceOrdinalCloglogRegr$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()

---

InferenceOrdinalCloglogRegr$set_custom_randomization_statistic_function()

Usage

InferenceOrdinalCloglogRegr$set_custom_randomization_statistic_function(
  custom_randomization_statistic_function
)

---

InferenceOrdinalCloglogRegr$set_custom_randomization_statistic_cpp()

Usage

InferenceOrdinalCloglogRegr$set_custom_randomization_statistic_cpp(fn)

---

InferenceOrdinalCloglogRegr$approximate_randomization_distribution_beta_hat_T()

Usage

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

---

InferenceOrdinalCloglogRegr$supports_rand_pval_for_incidence()

Usage

InferenceOrdinalCloglogRegr$supports_rand_pval_for_incidence()

---

InferenceOrdinalCloglogRegr$compute_rand_two_sided_pval()

Usage

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

---

InferenceOrdinalCloglogRegr$clone()

The objects of this class are cloneable with this method.

Usage

InferenceOrdinalCloglogRegr$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.