Probit Regression Inference for Incidence Responses

Fits a probit regression model for binary (incidence) responses: \(\Phi^{-1}(P(Y_i = 1)) = \beta_0 + \beta_T W_i + X_i^\top \gamma\), where \(\Phi\) is the standard normal CDF, \(W_i\) is the treatment indicator, and \(X_i\) are optional recorded covariates, by maximum likelihood (fast_probit_regression_cpp/ fast_probit_regression_weighted_cpp). Unlike InferenceIncidLogRegr's logit link, \(\hat\beta_T\) here is not an odds-ratio scale parameter: it is the treatment's additive effect on the latent standard-normal index underlying the binary outcome. likelihood_tier = "full": Wald, score, gradient, and likelihood-ratio tests are all available when the model converges, plus parametric-likelihood-bootstrap calibration of the likelihood-ratio test. A fit whose coefficients exceed max_abs_reasonable_coef in magnitude (a proxy for near-perfect separation) is cached as nonestimable rather than returned. Validity requires the usual probit assumptions: correctly specified linear predictor on the latent-normal scale, independence across subjects conditional on covariates, and no perfect/quasi-complete separation.

References

McCullagh, P., and Nelder, J. A. (1989). Generalized Linear Models (2nd ed.). Chapman and Hall/CRC, for the binomial GLM family and probit link.

See also

InferenceIncidLogRegr for the logit-link alternative with a log-odds-ratio estimand. Comparable Python API: statsmodels GLM (family=Binomial(link=probit())). See also: Probit model (Wikipedia).

Super class

Inference -> InferenceIncidProbitRegr

Methods

Public methods

• InferenceIncidProbitRegr$set_custom_randomization_statistic_function()

• InferenceIncidProbitRegr$set_custom_randomization_statistic_cpp()

• InferenceIncidProbitRegr$approximate_randomization_distribution_beta_hat_T()

• InferenceIncidProbitRegr$supports_rand_pval_for_incidence()

• InferenceIncidProbitRegr$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()

---

InferenceIncidProbitRegr$set_custom_randomization_statistic_function()

Usage

InferenceIncidProbitRegr$set_custom_randomization_statistic_function(
  custom_randomization_statistic_function
)

---

InferenceIncidProbitRegr$set_custom_randomization_statistic_cpp()

Usage

InferenceIncidProbitRegr$set_custom_randomization_statistic_cpp(fn)

---

InferenceIncidProbitRegr$approximate_randomization_distribution_beta_hat_T()

Usage

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

---

InferenceIncidProbitRegr$supports_rand_pval_for_incidence()

Usage

InferenceIncidProbitRegr$supports_rand_pval_for_incidence()

---

InferenceIncidProbitRegr$clone()

The objects of this class are cloneable with this method.

Usage

InferenceIncidProbitRegr$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

# \donttest{
seq_des = DesignSeqOneByOneBernoulli$new(n = 10, response_type = 'incidence')
for (i in 1:10) {
  seq_des$add_one_subject_to_experiment_and_assign(data.frame(x1 = rnorm(1)))
}
seq_des$add_all_subject_responses(rbinom(10, 1, 0.5))
inf = InferenceIncidProbitRegr$new(seq_des)
inf$compute_estimate()
#> [1] 0.7042166
# }