Ordered Probit Regression Inference for Ordinal Responses
Source:R/inference_ordinal_ordered_probit.R
InferenceOrdinalOrderedProbitRegr.RdFits a cumulative-probit ("ordered probit") model for ordinal responses:
\(\Phi^{-1}(P(Y_i \le k)) = \alpha_k - (\beta_T W_i + X_i^\top \gamma)\),
for cutpoints \(\alpha_1 < \cdots < \alpha_{K-1}\), where \(\Phi\) is
the standard normal CDF, \(W_i\) is the treatment indicator, and
\(X_i\) are optional recorded covariates, by maximum likelihood
(fast_ordinal_probit_regression_cpp/
fast_ordinal_probit_regression_with_var_cpp). As with binary
probit regression, \(\hat\beta_T\) is not an odds-ratio-scale parameter:
it is the treatment's effect on the latent standard-normal index
underlying the ordinal categories. 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. Validity requires the proportional/parallel
cutpoints assumption (a single \(\beta_T\) shared across all cutpoints)
in addition to the usual latent-normal-index assumption.
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$should_use_design_randomization_for_incidence()).
TRUE for every other case, including every non-incidence
response type. Public, self-contained (only reads already-set
instance state, no side effects), so InferenceSuite can
check this before attempting the sentinel instead of relying on
the stop() being silently swallowed into a pval = NA
"ok" row – the single source of truth for both this check and
compute_rand_two_sided_pval()'s own guard, so the two can
never drift apart.
Computes a randomization-based p-value.
Value
When debug = FALSE (default), a numeric vector of length r. When
debug = TRUE, a list with: values, errors (list of character
vectors, one per iteration), warnings (list of character vectors, one per
iteration), num_errors, num_warnings,
prop_iterations_with_errors, prop_iterations_with_warnings, and
prop_illegal_values.
A single logical.
Randomization p-value.
References
McCullagh, P. (1980). "Regression Models for Ordinal Data." Journal of the Royal Statistical Society, Series B, 42(2), 109-142, doi:10.1111/j.2517-6161.1980.tb01109.x , for the cumulative-link ordinal model family this class's probit link instantiates.
See also
InferenceOrdinalCauchitRegr,
InferenceOrdinalCloglogRegr
for other cumulative-link function choices on the same ordinal model
family. See also:
Ordinal
regression and Probit
model (Wikipedia).
Super class
Inference -> InferenceOrdinalOrderedProbitRegr
Methods
+ inherited public methods from Inference
Inference$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$supports()
InferenceOrdinalOrderedProbitRegr$approximate_randomization_distribution_beta_hat_T()
Usage
InferenceOrdinalOrderedProbitRegr$approximate_randomization_distribution_beta_hat_T(
r = 501,
delta = 0,
transform_responses = "none",
show_progress = TRUE,
permutations = NULL,
debug = FALSE,
zero_one_logit_clamp = .Machine$double.eps
)Arguments
rNumber of randomization vectors. Default 501.
rNumber of randomization vectors.
deltaThe null difference. Default 0.
deltaNull difference.
transform_responsesType of transformation. Default "none".
transform_responsesTransformation.
show_progressShow progress bar. Default TRUE.
show_progressShow progress.
permutationsPre-computed permutations. Default NULL.
permutationsPre-computed permutations.
debugIf
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. DefaultFALSE.zero_one_logit_clampThe clamping amount for exact 0 and 1 values when logging
zero_one_logit_clampThe clamping amount for exact 0 and 1 values when logging
InferenceOrdinalOrderedProbitRegr$compute_rand_two_sided_pval()
Usage
InferenceOrdinalOrderedProbitRegr$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$double.eps
)Arguments
rNumber of randomization vectors. Default 501.
rNumber of randomization vectors.
deltaThe null difference. Default 0.
deltaNull difference.
transform_responsesType of transformation. Default "none".
transform_responsesTransformation.
na.rmRemove NAs.
show_progressShow progress bar. Default TRUE.
show_progressShow progress.
permutationsPre-computed permutations. Default NULL.
permutationsPre-computed permutations.
zero_one_logit_clampThe clamping amount for exact 0 and 1 values when logging
zero_one_logit_clampThe clamping amount for exact 0 and 1 values when logging
Examples
# \donttest{
seq_des = DesignSeqOneByOneBernoulli$new(n = 10, response_type = 'ordinal')
for (i in 1:10) {
seq_des$add_one_subject_to_experiment_and_assign(data.frame(x1 = rnorm(1)))
}
seq_des$add_all_subject_responses(sample(1:4, 10, replace = TRUE))
inf = InferenceOrdinalOrderedProbitRegr$new(seq_des)
inf$compute_estimate()
#> [1] -0.1961553
# }