Stereotype Logit Regression Inference for Ordinal Responses

Fits Anderson's (1984) stereotype logit model for ordinal responses (see fast_stereotype_logit_cpp for the full reduced-rank multinomial-softmax formula and reparameterization): a single linear predictor \(\eta_i = \beta_T W_i + X_i^\top \gamma\) is scaled by a category-specific score \(\phi_k \in [0,1]\) (jointly estimated, monotone in \(k\)) in a softmax over all \(K\) categories, rather than assuming a single proportional/parallel effect across cuts as InferenceOrdinalContRatioRegr/ InferenceOrdinalKKCondAdjCatLogitRegr do. This makes the stereotype model a genuinely more flexible (multinomial-logit-like, reduced-rank) alternative to the standard proportional-odds/adjacent-category/continuation-ratio ordinal families, at the cost of a less directly interpretable treatment coefficient (\(\beta_T\) enters multiplicatively through the \(\phi_k\) scores rather than as a single additive log-odds-ratio). likelihood_tier = "full": likelihood-ratio, score, gradient, and Wald tests are all available when the model converges, plus parametric-likelihood-bootstrap calibration of the likelihood-ratio test. Bayesian-bootstrap inference is temporarily unavailable because the current non-uniform weighted hook fits a cumulative-logit surrogate rather than the stereotype likelihood. It will remain disabled until the native weighted stereotype-logit backend described in the package implementation plan lands.

References

Anderson, J. A. (1984). "Regression and Ordered Categorical Variables." Journal of the Royal Statistical Society, Series B, 46(1), 1-30, doi:10.1111/j.2517-6161.1984.tb01276.x , for the stereotype logit model.

See also

InferenceOrdinalContRatioRegr for a proportional (non-reduced-rank) ordinal alternative. See also: Ordinal regression (Wikipedia).

Super class

Inference -> InferenceOrdinalStereotypeLogitRegr

Methods

Public methods

• InferenceOrdinalStereotypeLogitRegr$set_custom_randomization_statistic_function()

• InferenceOrdinalStereotypeLogitRegr$set_custom_randomization_statistic_cpp()

• InferenceOrdinalStereotypeLogitRegr$approximate_randomization_distribution_beta_hat_T()

• InferenceOrdinalStereotypeLogitRegr$supports_rand_pval_for_incidence()

• InferenceOrdinalStereotypeLogitRegr$compute_rand_two_sided_pval()

• InferenceOrdinalStereotypeLogitRegr$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()

---

InferenceOrdinalStereotypeLogitRegr$set_custom_randomization_statistic_function()

Usage

InferenceOrdinalStereotypeLogitRegr$set_custom_randomization_statistic_function(
  custom_randomization_statistic_function
)

---

InferenceOrdinalStereotypeLogitRegr$set_custom_randomization_statistic_cpp()

Usage

InferenceOrdinalStereotypeLogitRegr$set_custom_randomization_statistic_cpp(fn)

---

InferenceOrdinalStereotypeLogitRegr$approximate_randomization_distribution_beta_hat_T()

Usage

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

---

InferenceOrdinalStereotypeLogitRegr$supports_rand_pval_for_incidence()

Usage

InferenceOrdinalStereotypeLogitRegr$supports_rand_pval_for_incidence()

---

InferenceOrdinalStereotypeLogitRegr$compute_rand_two_sided_pval()

Usage

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

---

InferenceOrdinalStereotypeLogitRegr$clone()

The objects of this class are cloneable with this method.

Usage

InferenceOrdinalStereotypeLogitRegr$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.