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underdisp 0.1.0

First public release. underdisp provides diagnostics and a unified family of estimators for underdispersed count data (conditional variance below the conditional mean), the case the Poisson and negative binomial defaults cannot represent. The likelihood core is implemented in C++.

Screening

• ud_screen(): at-risk dispersion diagnostic that benchmarks a fitted count against a zero-truncated Poisson under unit and period fixed effects, with a marginal statistic, a zero-truncated-Poisson at-risk statistic, and an over-conditioning guard. The at-risk threshold is available in two modes, ztp_threshold = "calibrated" (a fast n-dependent calibrated cutoff) and ztp_threshold = "bootstrap" (a parametric bootstrap of the fitted zero-truncated-Poisson null on the data’s own design, ztp_boot_B), and an optional native COM-Poisson comparator (run_comp).

Estimators

• cpb(): continuous parameter binomial (CPB) regression and its zero-truncated variant, with an interpretable observation-specific bound (the implied ceiling). C++ multistart estimation.
• cpb_fe(): high-dimensional fixed-effects CPB via a concentrated likelihood that matches the full-dummy likelihood to machine precision.
• hurdle_cpb() and zi_cpb(): two-part (participation logit + zero-truncated CPB intensity) and true zero-inflated mixture forms, each with fixed effects available in both equations.
• gec(): King’s generalized event count / Katz-family regression, a single model whose dispersion is estimated freely and spans underdispersion, equidispersion, and overdispersion, with gec_fe(), hurdle_gec(), and zi_gec() variants.
• count_reg(), hurdle_count(), zi_count(): matched Poisson, negative binomial, and COM-Poisson families sharing one interface, with fixed effects (including two-way), offsets, and truncated/hurdle/zero-inflated forms, for like-for-like comparison against the CPB and GEC families.

Inference

• Coefficient inference by a cold-multistart pairs (or cluster) bootstrap with percentile intervals; dispersion inference by a profile-likelihood interval for the shape parameter, which respects the feasibility boundary where the bootstrap distribution is skewed (alpha_confint()).
• Robust and clustered standard errors throughout, via a block bootstrap rather than a Hessian sandwich, since the CPB’s parameter-dependent support makes the Hessian unreliable. Fixed-effects bootstraps use normal-approximation intervals, because replicates share the incidental-parameters bias and percentile intervals would be off-center.

Bias-corrected fixed-effects estimation

• bias_correct = "jackknife" on the concentrated fixed-effects estimators (cpb_fe(), gec_fe(), and the fe = intensity of hurdle_cpb()): the split-panel jackknife (Dhaene & Jochmans 2015) removes the leading 1/T incidental-parameters bias of the dispersion parameter, validated by the package’s fixed-effects bias Monte Carlo (alpha bias at T = 6/10/20/40 falls from -.147/-.096/-.056/-.033 to -.038/-.022/-.016/-.009). The correction carries a VALIDITY GATE for the method’s time-homogeneity requirement: the time-split disagreement is compared against exchangeable unit-split placebo noise, and on panels where the two halves do not estimate a common parameter the correction is refused with an informative warning and the maximum-likelihood fit is returned. A refusal is diagnostic information about the panel, not an error.
• For separation in dummy-heavy participation equations, the hurdle factorizes: fit the participation stage with a dedicated bias-reduction package (logistf, brglm2) alongside the zero-truncated intensity from this package.

Comparison and testing

• compare_dispersion() and compare_models(): information-criteria and proper scoring-rule comparison across Poisson, negative binomial, COM-Poisson, and CPB (and their hurdle and zero-inflated forms), with type-safe rejection of non-package or mismatched objects.
• zi_test(): boundary-corrected likelihood-ratio test for zero-inflation (the plain model nested in the mixture at the boundary), for both the CPB and GEC families.

Quantities of interest

• predict(), implied_ceiling(), alpha_confint(), irr(), and first_difference(). Every first_difference() method in the package returns one unified "ud_fd" data frame (component, from, to, diff, lower, upper, method): single-equation fits report the mean, and the two-part/mixture models report the exact extensive/intensive decomposition (binary-stage probability, count-stage mean, marginal mean), with a stage argument on every two-part method to move the covariate in a single equation and a per-row method label recording the uncertainty source (stored bootstrap for cpb, refit bootstrap via B= for the CPB two-parts, delta-method where an analytic covariance exists). Unknown arguments error rather than being silently ignored.

Distributions and simulators

• Density, distribution, quantile, and random-generation functions for the package’s own families: dcpb/pcpb/qcpb/rcpb, dgec/pgec/qgec/rgec, dcompois/pcompois/qcompois/rcompois, plus the mixture simulators rhurdle_cpb() and rzicpb(). The standard zero-truncated, hurdle, and zero-inflated Poisson/negative-binomial forms are deliberately internal: CRAN already serves those families (e.g. VGAM), and the exported surface is reserved for what the package adds.
• simulate() methods for every model class (cpb, cpb_fe, gec, gec_fe, count_reg, hurdle_count, zi_count, hurdle_cpb, hurdle_gec, zi_cpb, zi_gec), with fitted() completed across the two-part and fixed-effects classes, so any fit plugs into DHARMa’s simulated-residual diagnostics via DHARMa::createDHARMa().

Panel tools and calibration

• mundlak(): correlated-random-effects device that augments a formula with unit means, model-agnostic across the estimators.
• score() and cv_score() (log score and ranked probability score, in sample and by cross-validation), rootogram() (Tukey hanging), and pit_hist() (non-randomized PIT histogram).

Numerical robustness

The estimators are hardened for the difficult likelihoods this package targets (near-boundary dispersion, zero-heavy and dummy-heavy panels):

• Multistart estimation with per-start restart-polishing, and, for the zero-inflated CPB, an expectation-maximization cross-check run alongside the direct maximum-likelihood multistart so the better optimum is kept, avoiding the degenerate zero-mass-collapse basin.
• Loud, estimator-backed fallbacks that degrade gracefully rather than returning NA: a Fisher-scoring fallback for the zero-truncated-Poisson screen when the default IRLS fit errors or silently diverges, and a ridge-regularized Fisher step in the bootstrap null on singular information matrices. Each fallback warns and reports the method actually used.
• Fitted-rate sanity guards that key on the pathology (diverged rates) rather than its correlates (iteration counts), and floored mixture likelihoods so a transient zero-probability iterate cannot produce a non-finite objective.
• Fit-rank–exact degrees of freedom in the at-risk screen and the mixture comparisons, so zero-heavy designs are neither over- nor under-penalized.

Data and integration

• Bundled peacekeeping dataset (UN peacekeeping contributions, a state-year roster with structural zeros).
• broom (tidy/glance/augment) methods for all model classes, and modelsummary / texreg table support.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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