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.

Computes the randomization distribution of the treatment effect estimate under the sharp null.

Whether compute_rand_two_sided_pval() is actually usable on this instance right now – FALSE exactly when it would stop(): an incidence-response instance with no custom randomization statistic and a design not eligible for design-randomization-based incidence inference (see private$should_use_design_randomization_for_incidence()). TRUE for every other case, including every non-incidence response type. Public, self-contained (only reads already-set instance state, no side effects), so InferenceSuite can check this before attempting the sentinel instead of relying on the stop() being silently swallowed into a pval = NA "ok" row – the single source of truth for both this check and compute_rand_two_sided_pval()'s own guard, so the two can never drift apart.

Computes a randomization-based p-value.

Value

When debug = FALSE (default), a numeric vector of length r. When debug = TRUE, a list with: values, errors (list of character vectors, one per iteration), warnings (list of character vectors, one per iteration), num_errors, num_warnings, prop_iterations_with_errors, prop_iterations_with_warnings, and prop_illegal_values.

A single logical.

Randomization p-value.

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$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$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
)

Arguments

r

Number of randomization vectors. Default 501.

r

Number of randomization vectors.

delta

The null difference. Default 0.

delta

Null difference.

transform_responses

Type of transformation. Default "none".

transform_responses

Transformation.

show_progress

Show progress bar. Default TRUE.

show_progress

Show progress.

permutations

Pre-computed permutations. Default NULL.

permutations

Pre-computed permutations.

debug

If TRUE, return a list with the distribution values and per-iteration diagnostics including error messages, warning messages, counts of each, and summary proportions for iterations with errors, warnings, and illegal (non-finite) values. Runs serially. Default FALSE.

zero_one_logit_clamp

The clamping amount for exact 0 and 1 values when logging

zero_one_logit_clamp

The clamping amount for exact 0 and 1 values when logging

---

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
)

Arguments

r

Number of randomization vectors. Default 501.

r

Number of randomization vectors.

delta

The null difference. Default 0.

delta

Null difference.

transform_responses

Type of transformation. Default "none".

transform_responses

Transformation.

na.rm

Remove NAs.

show_progress

Show progress bar. Default TRUE.

show_progress

Show progress.

permutations

Pre-computed permutations. Default NULL.

permutations

Pre-computed permutations.

zero_one_logit_clamp

The clamping amount for exact 0 and 1 values when logging

zero_one_logit_clamp

The clamping amount for exact 0 and 1 values when logging

---

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.