Ordinal KK CLMM (Cauchit link)

Cumulative-link random-intercept mixed model for ordinal responses under a KK matching-on-the-fly design, using the cauchit (inverse-Cauchy-CDF) link: \(\tan(\pi (P(Y_i \le k) - 1/2)) = \alpha_k - (\beta_T W_i + X_i^\top \gamma) - b_{g(i)}\), \(b_g \sim N(0, \sigma_b^2)\), where \(g(i)\) is subject \(i\)'s matched-pair group id. The cauchit link's heavy-tailed latent distribution makes it more robust than logit/probit to a small number of subjects near the response's extreme categories. See InferenceAbstractKKOrdinalCLMM for the shared model-fitting, caching, and likelihood-tier contract common to all four link-function siblings; this class supplies only the link-function choice (private$clmm_link() == "cauchit").

Super classes

Inference -> InferenceAbstractKKOrdinalCLMM -> InferenceOrdinalKKCLMMCauchit

Methods

Public methods

• InferenceOrdinalKKCLMMCauchit$new()

• InferenceOrdinalKKCLMMCauchit$clone()

+ inherited public methods from InferenceAbstractKKOrdinalCLMM

• InferenceAbstractKKOrdinalCLMM$approximate_bayesian_bootstrap_distribution_beta_hat_T()
• InferenceAbstractKKOrdinalCLMM$approximate_bootstrap_distribution_beta_hat_T()
• InferenceAbstractKKOrdinalCLMM$approximate_jackknife_distribution_beta_hat_T()
• InferenceAbstractKKOrdinalCLMM$approximate_m_out_of_n_bootstrap_distribution_beta_hat_T()
• InferenceAbstractKKOrdinalCLMM$approximate_rand_bootstrap_distribution_beta_hat_T()
• InferenceAbstractKKOrdinalCLMM$approximate_randomization_distribution_beta_hat_T()
• InferenceAbstractKKOrdinalCLMM$approximate_subsampling_distribution_beta_hat_T()
• InferenceAbstractKKOrdinalCLMM$compute_asymp_confidence_interval()
• InferenceAbstractKKOrdinalCLMM$compute_asymp_two_sided_pval()
• InferenceAbstractKKOrdinalCLMM$compute_bayesian_bootstrap_confidence_interval()
• InferenceAbstractKKOrdinalCLMM$compute_bayesian_bootstrap_two_sided_pval()
• InferenceAbstractKKOrdinalCLMM$compute_bootstrap_confidence_interval()
• InferenceAbstractKKOrdinalCLMM$compute_bootstrap_two_sided_pval()
• InferenceAbstractKKOrdinalCLMM$compute_estimate()
• InferenceAbstractKKOrdinalCLMM$compute_estimate_with_bootstrap_weights()
• InferenceAbstractKKOrdinalCLMM$compute_jackknife_bias_estimate()
• InferenceAbstractKKOrdinalCLMM$compute_jackknife_estimate()
• InferenceAbstractKKOrdinalCLMM$compute_jackknife_std_error()
• InferenceAbstractKKOrdinalCLMM$compute_jackknife_wald_confidence_interval()
• InferenceAbstractKKOrdinalCLMM$compute_jackknife_wald_two_sided_pval()
• InferenceAbstractKKOrdinalCLMM$compute_m_out_of_n_bootstrap_confidence_interval()
• InferenceAbstractKKOrdinalCLMM$compute_m_out_of_n_bootstrap_two_sided_pval()
• InferenceAbstractKKOrdinalCLMM$compute_rand_bootstrap_confidence_interval()
• InferenceAbstractKKOrdinalCLMM$compute_rand_bootstrap_two_sided_pval()
• InferenceAbstractKKOrdinalCLMM$compute_rand_confidence_interval()
• InferenceAbstractKKOrdinalCLMM$compute_rand_two_sided_pval()
• InferenceAbstractKKOrdinalCLMM$compute_subsampling_confidence_interval()
• InferenceAbstractKKOrdinalCLMM$compute_subsampling_sensitivity()
• InferenceAbstractKKOrdinalCLMM$compute_subsampling_two_sided_pval()
• InferenceAbstractKKOrdinalCLMM$compute_wald_confidence_interval()
• InferenceAbstractKKOrdinalCLMM$compute_wald_two_sided_pval()
• InferenceAbstractKKOrdinalCLMM$get_mod()
• InferenceAbstractKKOrdinalCLMM$get_summary()
• InferenceAbstractKKOrdinalCLMM$get_supported_bayesian_bootstrap_ci_types()
• InferenceAbstractKKOrdinalCLMM$get_supported_bayesian_bootstrap_pval_types()
• InferenceAbstractKKOrdinalCLMM$get_supported_bootstrap_ci_types()
• InferenceAbstractKKOrdinalCLMM$get_supported_bootstrap_pval_types()
• InferenceAbstractKKOrdinalCLMM$get_supported_rand_bootstrap_ci_types()
• InferenceAbstractKKOrdinalCLMM$get_supported_rand_bootstrap_pval_types()
• InferenceAbstractKKOrdinalCLMM$get_supported_testing_types()
• InferenceAbstractKKOrdinalCLMM$select_optimal_b_subsampling()
• InferenceAbstractKKOrdinalCLMM$select_optimal_m_out_of_n_bootstrap()
• InferenceAbstractKKOrdinalCLMM$set_custom_randomization_statistic_cpp()
• InferenceAbstractKKOrdinalCLMM$set_custom_randomization_statistic_function()
• InferenceAbstractKKOrdinalCLMM$set_testing_type()
• InferenceAbstractKKOrdinalCLMM$supports_rand_pval_for_incidence()

+ inherited public methods from Inference

• Inference$capabilities()
• Inference$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$is_nonestimable()
• Inference$set_optimization_alg()
• Inference$set_seed()
• Inference$supports()

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InferenceOrdinalKKCLMMCauchit$new()

Initialize the cauchit-link ordinal KK CLMM subclass; see the shared ordinal mixed-model contract in InferenceAbstractKKOrdinalCLMM.

Usage

InferenceOrdinalKKCLMMCauchit$new(
  des_obj,
  model_formula = NULL,
  use_rcpp = TRUE,
  verbose = FALSE,
  smart_cold_start_default = NULL
)

Arguments

des_obj

A completed Design object.

model_formula

Optional formula for covariate adjustment.

use_rcpp

Use internal Rcpp implementation (default TRUE).

verbose

Print messages?

smart_cold_start_default

Use smart cold start values?

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InferenceOrdinalKKCLMMCauchit$clone()

The objects of this class are cloneable with this method.

Usage

InferenceOrdinalKKCLMMCauchit$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

# \donttest{
seq_des = DesignSeqOneByOneKK14$new(n = 10, response_type = 'ordinal')
for (i in 1:10) {
  seq_des$add_one_subject_to_experiment_and_assign(data.frame(x1 = rnorm(1), x2 = rnorm(1)))
}
seq_des$add_all_subject_responses(sample(1:4, 10, replace = TRUE))
inf = InferenceOrdinalKKCLMMCauchit$new(seq_des)
inf$compute_estimate()
#> [1] -0.04076549
# }