Quasi-Poisson Regression Inference for Count Responses

Fits a Poisson log-link mean model, \(\log E[Y_i \mid x_i] = x_i^\top\beta\), for count responses using the treatment indicator and, optionally, all recorded covariates as predictors, via fast_quasipoisson_regression_with_var_cpp — see that page for the full model and the Pearson-dispersion-scaled ("quasi-Poisson") variance formula, \(\widehat{\mathrm{Var}}(\hat\beta_k) = \hat\phi\,[(X^\top \hat{W}X)^{-1}]_{kk}\), which corrects standard errors for overdispersion (\(\mathrm{Var}(Y_i) > E[Y_i]\)) relative to the strict Poisson assumption without changing the point estimate \(\hat\beta\). This class has no likelihood-ratio/score/gradient testing capability (likelihood_tier = "quasi"): the dispersion-scaled quasi-likelihood is not a normalized model likelihood, so only Wald inference is available. Rank-deficient covariate columns are dropped automatically before fitting (via private$fit_with_hardened_qr_column_dropping()).

Estimand. Composes MarginalEstimand (set_estimand()/get_estimand()/get_supported_estimands()). Under the default estimand = "conditional", \(\hat\beta_T\) is the treatment log-rate-ratio. Under "marginal_mean_diff" it is the g-computed difference in the average fitted count under treatment vs. control, \(\frac{1}{n}\sum_i \{\exp(x_{i1}^\top\hat\beta) - \exp(x_{i0}^\top\hat\beta)\}\), with every subject plugged in at treatment 1 and 0. "marginal_ratio" is the log of the corresponding ratio, which for this log-link family equals the conditional \(\hat\beta_T\) exactly (there is no treatment-by-covariate term), so it is offered for estimand-API consistency; its delta-method SE equals the conditional SE. Under a marginal estimand the standard error is the delta-method SE against the dispersion-scaled coefficient covariance \(\hat\phi (X^\top \hat W X)^{-1}\), i.e. the plain-Poisson marginal SE inflated by \(\sqrt{\hat\phi}\), with a normal reference (degrees of freedom Inf). Switching the estimand is a pure post-fit transform of the cached fit, never a refit. The Bayesian-bootstrap weighted refit is not estimand-aware: it always targets the conditional coefficient.

Super class

Inference -> InferenceCountQuasiPoisson

Methods

Public methods

• InferenceCountQuasiPoisson$new()

• InferenceCountQuasiPoisson$compute_estimate()

• InferenceCountQuasiPoisson$compute_estimate_with_bootstrap_weights()

• InferenceCountQuasiPoisson$compute_asymp_confidence_interval()

• InferenceCountQuasiPoisson$compute_asymp_two_sided_pval()

• InferenceCountQuasiPoisson$clone()

+ 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()

---

InferenceCountQuasiPoisson$new()

Uses the shared randomization two-sided p-value contract; see InferenceRand.

Initialize a quasi-Poisson regression inference object for a completed design with a count, uncensored response.

Usage

InferenceCountQuasiPoisson$new(
  des_obj,
  model_formula = NULL,
  verbose = FALSE,
  smart_cold_start_default = NULL,
  harden = TRUE
)

Arguments

des_obj

A completed Design object with a count response.

model_formula

Optional formula for covariate adjustment. If NULL (default), the formula from the design object is used and its pre-computed design matrix is reused. If a formula is provided, a new design matrix is constructed from the design's imputed covariates.

verbose

Whether to print progress messages.

smart_cold_start_default

Whether to use smart cold start values.

harden

Whether to apply robustness measures.

---

InferenceCountQuasiPoisson$compute_estimate()

Computes the quasi-Poisson point estimate via fast_quasipoisson_regression_with_var_cpp (see class documentation for the full model). Under the default estimand = "conditional" this is the treatment coefficient \(\hat\beta_T\); under "marginal_mean_diff" or "marginal_ratio" (set via set_estimand()) it is the g-computed marginal mean difference / log ratio, a pure post-fit transform of the same cached fit (no refit). Rank-deficient covariate columns are dropped before fitting.

Usage

InferenceCountQuasiPoisson$compute_estimate(estimate_only = FALSE)

Arguments

estimate_only

If TRUE, skip variance calculations.

---

InferenceCountQuasiPoisson$compute_estimate_with_bootstrap_weights()

Recomputes the Poisson-mean-model treatment estimate under subject/block bootstrap weights (via fast_poisson_regression_weighted_cpp), used by the Bayesian bootstrap and related weighted-resampling machinery; see InferenceBayesianBootstrap. When estimate_only = FALSE, also computes a weighted Pearson-dispersion-scaled standard error (fixed 2026-09-07 – previously always NA regardless of estimate_only, which starved the Bayesian-bootstrap studentized/BCa variants of a per-replicate SE and left them NA on the large majority of calls). The weighted refit always targets the conditional treatment coefficient, whatever the active estimand (it is not estimand-aware).

Usage

InferenceCountQuasiPoisson$compute_estimate_with_bootstrap_weights(
  subject_or_block_weights,
  estimate_only = FALSE
)

Arguments

subject_or_block_weights

Bootstrap weights at the subject or block level.

estimate_only

If TRUE, skip the dispersion-correction computation.

---

InferenceCountQuasiPoisson$compute_asymp_confidence_interval()

Computes a \(1-\alpha\) level Wald confidence interval for the active estimand. Under the default conditional estimand this is the quasi-Poisson treatment coefficient \(\hat\beta_T\) with the Pearson-dispersion-scaled standard error from fast_quasipoisson_regression_with_var_cpp (see class documentation); under a marginal estimand it is the g-computed functional with its delta-method standard error. Both use a normal reference. See InferenceAsymp for the shared asymptotic confidence-interval contract this delegates to.

Usage

InferenceCountQuasiPoisson$compute_asymp_confidence_interval(alpha = 0.05)

Arguments

alpha

Confidence level.

---

InferenceCountQuasiPoisson$compute_asymp_two_sided_pval()

Computes a two-sided Wald p-value testing \(H_0: \beta_T = \code{delta}\) under the conditional estimand, or that the active marginal functional equals delta under a marginal estimand, from the same standard error used by $compute_asymp_confidence_interval() (normal reference). See InferenceAsymp for the shared asymptotic two-sided p-value contract this delegates to.

Usage

InferenceCountQuasiPoisson$compute_asymp_two_sided_pval(delta = 0)

Arguments

delta

Null treatment effect value.

---

InferenceCountQuasiPoisson$clone()

The objects of this class are cloneable with this method.

Usage

InferenceCountQuasiPoisson$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

# \donttest{
seq_des = DesignSeqOneByOneBernoulli$new(n = 10, response_type = 'count')
for (i in 1:10) {
  seq_des$add_one_subject_to_experiment_and_assign(data.frame(x1 = rnorm(1)))
}
seq_des$add_all_subject_responses(rpois(10, 2))
inf = InferenceCountQuasiPoisson$new(seq_des)
inf$compute_estimate()
#> [1] -0.2672812
# }