Cauchit Regression Inference for Ordinal Responses

Cauchit-link cumulative-odds ordinal regression: \(P(Y \le k \mid w, x) = F_{\mathrm{Cauchy}}(\alpha_k - \beta_T w - \beta_X^\top x)\), where \(F_{\mathrm{Cauchy}}\) is the standard Cauchy CDF, \(\alpha_k\) are category-specific cutpoints, and \(\beta_T\) is the treatment log-odds coefficient on the cauchit scale (proportional-odds-style shift common to all categories). Fit by maximum likelihood. The heavy-tailed Cauchy link is markedly less sensitive to outlying/extreme response categories than the logit or probit link, at the cost of a less familiar effect-size interpretation. likelihood_tier = "full": exposes likelihood-ratio, score, gradient, and parametric-likelihood-bootstrap inference in addition to the Wald/asymptotic and Bayesian-bootstrap paths.

References

Agresti, A. (2010). Analysis of Ordinal Categorical Data (2nd ed.). Wiley. Ch. 3-4 (cumulative link models).

See also

https://en.wikipedia.org/wiki/Ordinal_regression, https://www.statsmodels.org/stable/discretemod.html for an analogous Python cumulative-link API.

Super class

Inference -> InferenceOrdinalCauchitRegr

Methods

Public methods

• InferenceOrdinalCauchitRegr$set_custom_randomization_statistic_function()

• InferenceOrdinalCauchitRegr$set_custom_randomization_statistic_cpp()

• InferenceOrdinalCauchitRegr$approximate_randomization_distribution_beta_hat_T()

• InferenceOrdinalCauchitRegr$supports_rand_pval_for_incidence()

• InferenceOrdinalCauchitRegr$compute_rand_two_sided_pval()

• InferenceOrdinalCauchitRegr$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()

---

InferenceOrdinalCauchitRegr$set_custom_randomization_statistic_function()

Usage

InferenceOrdinalCauchitRegr$set_custom_randomization_statistic_function(
  custom_randomization_statistic_function
)

---

InferenceOrdinalCauchitRegr$set_custom_randomization_statistic_cpp()

Usage

InferenceOrdinalCauchitRegr$set_custom_randomization_statistic_cpp(fn)

---

InferenceOrdinalCauchitRegr$approximate_randomization_distribution_beta_hat_T()

Usage

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

---

InferenceOrdinalCauchitRegr$supports_rand_pval_for_incidence()

Usage

InferenceOrdinalCauchitRegr$supports_rand_pval_for_incidence()

---

InferenceOrdinalCauchitRegr$compute_rand_two_sided_pval()

Usage

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

---

InferenceOrdinalCauchitRegr$clone()

The objects of this class are cloneable with this method.

Usage

InferenceOrdinalCauchitRegr$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.