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Converting a fitted ceiling to an integer is now guarded against
values outside the range of int. The CPB’s ceiling is
lambda / (1 - alpha) and the GEC’s is
mu / (1 - delta); both diverge as the dispersion parameter
approaches its equidispersed limit, which an optimizer reaches
routinely, and the conversion was undefined behaviour there. CRAN’s
macOS sanitizer build reported it in cpb_pmf.h and
cpb_fe.cpp. All six conversions of this kind, including two
the sanitizer did not reach, now cap the ceiling at
max.support + 1 first, through a single rule in
src/support_cap.h.
A ceiling past max.support was already treated as
infeasible, on both of the platforms whose out-of-range conversions
differ, so fitted values are unchanged: every cross-sectional and
fixed-effects CPB fit, every GEC fit without fixed effects, and the
calibrated interval reproduce bit for bit. The exception is
gec_fe() on data whose dispersion is driven to the Katz
limit, where the breakpoint scan now runs from a defined bound and the
optimizer can settle a few parts in 10^8 away.
count_reg(), hurdle_count(), and
zi_count() gain four underdispersed families through the
same interface, each inheriting fixed effects, zero-truncation, hurdle
and zero-inflated forms, offsets, weights, the sandwiches, proper
scores, DHARMa simulation, and the QoI methods: "mpcmp"
(the COM-Poisson in Huang’s 2017 mean parameterization, with the rate
solving E(Y) = mu found in C++), "genpois" (the Consul-Jain
generalized Poisson with constant dispersion lambda, renormalized on its
finite support when lambda < 0), "gammacount"
(Winkelmann’s 1995 renewal-process model with gamma waiting times), and
"doublepois" (Efron’s 1986 double Poisson with the exact
normalizing constant). Every family’s pmf was checked against an
independent implementation (rmutil, gamlss.dist, VGAM) to machine
precision, and the generalized-Poisson and mean-parameterized
COM-Poisson log-likelihoods reproduce glmmTMB’s genpois and
compois fits exactly.dgammacount(), ddoublepois(),
dgenpois() and their p/q/r companions; the COM-Poisson
functions accept mu = for the mean parameterization.dispersion_test(): the likelihood-ratio test of a
fitted family’s dispersion parameter against its Poisson value on the
fitted design (fixed effects included, the unit effects profiled out of
the Poisson null), with two-sided or directional alternatives by the
signed root and the boundary mixture where the Poisson value is on the
boundary (CPB, negative binomial); and the Cameron-Trivedi
auxiliary-regression test for a Poisson fit. The p-value is a parametric
bootstrap under the fitted Poisson (B, cores)
whenever the Poisson value is on the boundary of the family’s parameter
space (CPB, negative binomial) or the fit has unit fixed effects; where
it is interior, the asymptotic p-value is used unless the first-order
bias from the null’s estimated mean parameters, p / sqrt(2n) standard
deviations, pushes a 5% test’s size above 6%. summary() of
a CPB fit flags its asymptotic p-value.ud_screen(): in
ztp_threshold = "bootstrap" mode the NB-vs-Poisson p-value
is a parametric bootstrap under the fitted Poisson
(nb_boot) when the mean model is within the comparator
gates; the fast mode’s asymptotic value is labeled conservative. The
bootstrap restores the random-number state, so the at-risk threshold and
every other result are unchanged.dispersion_profile(): the empirical conditional
variance-to-mean ratio by bins of the fitted mean against the ratio each
fitted family implies, with a plot() method, so the
mechanism behind an underdispersed outcome (a hard ceiling, regular
event timing, a soft tail) can be read off the data.calibrate_alpha(): an opt-in calibration of the
interval for the CPB dispersion parameter. The support of the CPB moves
with the parameters through the log-ceiling coefficients, which behave
like endpoint parameters, and the estimate of alpha
inherits a bias toward zero from them; the first-order (chi-square)
profile interval therefore covers about 0.90 to 0.94 in simulations from
the CPB, with its misses on the upper side.
calibrate_alpha(fit, B, cores, seed) stores the
parametric-bootstrap distribution of the signed root of the profile
likelihood ratio in the fit, and alpha_confint(),
confint(), implied_ceiling() and
summary() then report the interval cut at its quantiles
(0.92 to 0.96 in the same simulations, misses balanced). The responses
are drawn once on the calling process and the refits use no random
numbers, so the result does not depend on cores. It is
refused, with the reason, for a fit at the max.support
guard, weights that are not whole numbers, and a fit saved by 0.1.0.
With few distinct covariate patterns the first-order interval already
covers at its level and the calibration is not needed. Without it the
accessors report the first-order interval, and
attr(, "method") and summary() say which one
is shown.weights = (frequency weights) on every estimator; a
weight of w is equivalent to w copies of the row in the likelihood, the
information, the score products, and the bootstrap, and
nobs() returns the weight total. In the parametric
bootstraps (dispersion_test(),
calibrate_alpha()) a row of weight w contributes w
independent simulated responses; weights that are not whole numbers have
no such replicate data, so dispersion_test() then reports
the asymptotic p-value with a note.cores = on every bootstrap, the parametric-bootstrap
screen threshold, cv_score(), and the refit first
differences: replicates run on a socket cluster seeded from the calling
session.fitted(), predict(type = "response"),
residuals(), and
first_difference(quantity = "mean") for cpb,
cpb_fe, and the hurdle-CPB intensity now report the exact
mean of the fitted distribution (a finite sum of the renormalized pmf,
and the conditional mean E(Y | Y >= 1) for zero-truncated fits), as
gec() and the matched families already did. The rate
parameter exp(x’b) equals the mean only when lambda/(1-alpha) is an
integer; it remains available as $rate and
predict(type = "rate"). The same holds for the generalized
event count: delta is the Katz dispersion parameter, which
is the variance-to-mean ratio on an unbounded support, and
exp(x'b) is the rate of the recursion.count_reg() fits report E(Y | Y >=
1).confint() for every model class (bootstrap percentile,
normal-approximation from the bootstrap, or Wald from the analytic
covariance, one rule per inference type); vcov() for the
hurdle and zero-inflated classes; implied_ceiling() for
cpb_fe; irr() and
first_difference() on a cpb fit without a
bootstrap return point estimates with method = "none";
vcov() returns NULL rather than an error when
no inference was requested.irr() labels the binary stage
"participation" (hurdle) or "inflation"
(zero-inflated), which point in opposite directions.extract() methods for count_reg,
hurdle_count, zi_count; the methods for every
class now attach to texreg’s generic (in 0.1.0 the registration silently
failed and tables fell back to broom), and the count families label
their dispersion row by the parameter.tidy() for the two-part classes prefixes each term by
its component, so modelsummary() lays the table out without
a shape argument.predict(), score(), and the QoI methods
rebuild a newdata model matrix in the fit’s own factor
coding (stored levels and contrasts) and align it to the coefficients by
name; a factor whose reference level was set through its contrasts
attribute (as in AER’s NMES1988) is no longer re-coded on
newdata, and a coding mismatch is refused instead of
multiplied by position.offset() term and a pscl-style
y ~ x | z formula are refused with a message naming
offset =, participation =, and
zero =; rows whose unit identifier is missing are dropped
like other incomplete rows; the screen’s generalized-Poisson comparator
is the package’s own family, so it can report underdispersion, and it is
gated by comp_max_par/comp_max_n like the
COM-Poisson (a full fit, not a diagnostic, on a dummy-heavy design);
print.gec() labels the dispersion direction by the
likelihood-ratio test; count_reg(fe =) hides the absorbed
dummies and warns when cluster is the fixed-effects
variable; standard errors from a Hessian that is not positive definite
are NA with a warning; the generalized Poisson’s support is
capped for negative dispersion; score() honours frequency
weights; the auxiliary test is weighted; the parallel driver draws its
cluster seed eagerly, so consecutive cores > 1
bootstraps differ.converged is stored by every class and reported by
print()/summary() when it is
FALSE; a matched-family fit whose optimizer never left the
infeasible plateau (a fitted mean outside [1e-12, 1e8]) is
reported as not converged with a warning, and its log-likelihood is
-Inf, instead of returning the sentinel as a
likelihood.gec()
or count_reg() fit, as score(),
rootogram(), pit_hist(), and
cv_score() use it, is the fit’s own zero-truncated pmf
normalized over the full support (in 0.1.0 the Katz pmf was scored
untruncated and the count families renormalized over the observed
range), so the in-sample log score equals -logLik/n for
every class; fitted() on a hurdle_gec is the
exact conditional mean that predict() returns.cv_score(), rootogram(),
pit_hist(), and dispersion_profile() apply
frequency weights as score() does, so a row of weight w
counts as w copies of itself: the rootogram’s observed and expected
frequencies, the PIT histogram, the dispersion profile’s bins (equal
weight, rows kept whole) and bin means, and, through a new
weights argument, the mean held-out scores of
cv_score() and score(newdata =).
rootogram() no longer fails when kmax exceeds
the largest count.pit_hist() read the lower bound F(y - 1) out of row
order wherever a zero count preceded a positive one, so its histogram
was wrong for data with zeros; the bound is now looked up row by
row.ud_screen() reports the NB-vs-Poisson likelihood ratio
at its boundary value 0 when glm.nb() stops short of the
Poisson limit, and prints “at the Poisson boundary” there rather than an
overdispersion reading.participation:/intensity: for the hurdles and
count:/zero: for the zero-inflated models, in
vcov(), confint(), tidy(), and
the texreg tables, so a term read off a table indexes the covariance and
the interval.cluster is checked for its length and for
missing values by every estimator before it is used (the fixed-effects
and two-part estimators recycled or padded a short vector in 0.1.0), and
a row dropped for a missing unit identifier drops its entry of a vector
offset, weights, or cluster with
it; hurdle_count() selects the cluster-robust covariance
when cluster is supplied, as its siblings do, and accepts a
vector cluster aligned to the data; zi_cpb()
and zi_gec() refuse a non-integer response instead of
flooring it; zi_cpb(), zi_count(), and
zi_gec() work on scaled covariates with a Nelder-Mead
polish like every other estimator (the unscaled joint fit of
zi_count() could stop at its starting values: on lme4’s
grouseticks it stopped 4.4 log-likelihood units below
pscl’s optimum); summary.zi_count() prints the stored
inflation standard errors; every bootstrapping summary states how many
replicates converged; count_reg() and
zi_count() store $fitted.values on the mean
scale and the natural parameter as $mu.cores > 1 attach the
package, so a cv_score() fit function that names
cpb() or count_reg() unqualified runs on
them.NA standard
errors).predict() with newdata returns
NA for a row whose covariate or offset is missing, as
predict.glm() does, instead of failing inside the
distribution routines. A column holding only missing values (which R
reads as logical) is treated as a missing value of the fitted variable’s
type, and a variable supplied with a different type than in the fitting
data is refused with a message that says so.alpha is traced
by continuation with a feasibility-repaired start at each
alpha, and the profile at each alpha is
maximized with the fit’s own multistart (BFGS, Nelder-Mead polish,
perturbed restarts), so the lower limit is the re-maximized profile’s
crossing point; the interval is one-sided only when the profile has not
dropped to the cut by alpha = 0.005. Each limit is the
outermost crossing of its cut (the profile is a saw-tooth, so the set
above a cut need not be connected), and a cut deeper than the stored
trace, as at a level above 0.995, re-runs the trace instead of returning
the parameter bounds.rcpb(truncated = TRUE) warns when a rate’s ceiling
lambda / (1 - alpha) is below 1: the zero-truncated CPB
does not exist there, and the draw of 1 it returns has probability zero
under the stated parameters.max.support defaults to
max(500, 10 * max(y)); a fit whose largest implied ceiling
reaches the guard warns and records $support_binding; a fit
whose every start is infeasible errors instead of returning the starting
values; a CPB fit that the guard stops short of its Poisson limit
reports the likelihood-ratio statistic at its boundary value 0.1 - alpha, and the objective drops at every such
breakpoint), so its supremum sits at an interior critical point of a
tooth or at the left limit of a breakpoint; the inner search enumerates
the breakpoints within a window of the envelope’s peak (as wide as the
widest tooth in the unit) and refines inside whole teeth by golden
section; every evaluation searches each unit afresh, so the concentrated
likelihood is a function of the parameters alone. It is continuous in
the dispersion parameter but can jump in the slopes where a unit sits on
its feasibility floor, so the outer optimizer is a deterministic
multistart: BFGS with the analytic envelope gradient (the breakpoint a
unit sits at is tracked in the gradient), a Nelder-Mead polish, and two
perturbed restarts; ?cpb_fe states the size of the
alternative optima. The Katz family below delta = 1 has a
finite support too, but its likelihood only kinks at an integer ceiling
(the entering point’s mass grows from zero), so gec_fe()
maximizes each unit’s unimodal objective by golden section on an
expanding bracket, with the feasibility floor exact (support
0..ceiling(mu/(1-delta))). The compiled code asserts the
unit index against the design, and the fits use only the estimation
rows, so rows dropped for missing values no longer misalign the unit
blocks.cpb() documents the discontinuity of the CPB
log-likelihood and the deterministic multistart that maximizes it (BFGS
from the Poisson solution at each alpha.start, Nelder-Mead
polish, feasibility-repaired restarts); the mean-parameterized
COM-Poisson tabulates its log-factorials.(n - k)/(k + 1) (1 - alpha)/alpha, so the sum runs over the
body of the distribution and stops where the terms fall below relative
precision on either side), shared by the pooled likelihoods and the
concentrated fixed-effects likelihood and gradient. A likelihood
evaluation costs the width of the pmf rather than its ceiling: on counts
in the hundreds one evaluation of the concentrated objective takes 0.04
s instead of 2.6 s, and the pooled objective is 45 times cheaper. The R
implementation of the pmf keeps the direct lgamma form as the
independent check (agreement to 5e-10 across alpha from 0.01 to 0.999
and rates from 0.05 to 2,000).cpb() fit is the
maximum of the fit’s own profile in alpha: the profile is
traced by continuation on both sides of the estimate (the slopes
re-maximized at each step from the neighbouring solution and from the
Poisson slopes, with a finer pass next to the estimate) until it has
dropped four log-likelihood units, and a trace point above the
multistart’s value restarts the fit from there; the multistart itself
runs from nine values of alpha and ends with an exact
breakpoint search in alpha at the fitted slopes, since the
teeth of the surface in alpha are thinner than any grid.
confint() and summary() read the profile
interval off the stored trace. On small samples the multistart alone
could stop on a lower tooth with alpha off by 0.1; the
remaining differences against a dense grid of starts are of the size of
the jumps (below 0.005 log-likelihood units on 12 samples of 72
zero-truncated counts). Unit intercepts belong in cpb_fe(),
which solves them exactly; a pooled fit with many dummy columns can stop
short of it (0.14 log-likelihood units on pscl’s prussian
with 14 corps dummies).cpb_fe() locates the peak of a
unit’s smooth part to 1e-6 (in 0.1.1’s first candidate the twelve
golden-section steps left an error of 1.6e-3, wider than a tooth at
ceilings above a few hundred, so the wrong tooth could be searched) and
searches the neighbouring tooth when the interior optimum sits at a
tooth’s end.max.support is
infeasible in the likelihood, a fit whose fitted support reaches the
guard warns and records $support_binding, and
predict(), dgec(), and pgec()
return NA with a warning for such a rate (in 0.1.0 the pmf
was silently renormalized over 0..max.support, so a
prediction far outside the fitted range was too small).mu = at strong underdispersion the rate exceeds it and the
pmf was wrong), and the d/p/q/r functions return NA for a
non-finite rate..ud_nm_polish() chains its restarts until a restart
gains less than the tolerance, as documented (the first candidate
stopped after one).offset, weights, or
cluster is refused; cluster supplied without a
bootstrap is announced; a cluster bootstrap with one cluster is refused
and with fewer than thirty warned.score() raises kmax to the largest
held-out count, and its predicted distributions carry the fit’s offset
(the in-sample log score equals -logLik/n for every class);
the hurdle intensities are zero-truncated over the full support;
first_difference() holds an offset at its mean and refuses
a variable that enters an interaction; the Katz recursion runs at least
to the observed count before its tail is dropped, so far-tail counts
under an unbounded member get their small probability rather than an
infeasibility sentinel; integer ceilings are feasible (floor with a
tolerance) in the C++ and the R pmf alike; the cluster-robust sandwich
carries the G/(G-1) factor.zi_cpb() records the user’s call;
predict() on gec and gec_fe uses
the stored factor levels; the exported d/p/q/r functions return
numeric(0) for zero-length input and refuse a vector
dispersion parameter.lm() and glm() do, so data subset from a
larger set no longer trip the rank-deficiency refusal on an empty
level.max.support, inner_it,
alpha.start, and B (with
se = "bootstrap") are checked on entry and refused by name
before any fitting: a support below 1 or beyond the integer range, a
fractional or negative count, fewer than two bootstrap replicates, a
start outside (0, 1).zi_test() fits from a formula, and the hurdle arm
of compare_dispersion() no longer repeat it, and a
gec() or gec_fe() fit no longer issues it
twice.weights, cores, and unknown-argument
checks on the matched families (misspelled arguments are errors);
inst/CITATION; a pkgdown site at
https://bagozzib.github.io/underdisp/ and GitHub Actions running the
full test suite (including the batteries skipped on CRAN) on five
platforms.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++.
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).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.alpha_confint()).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.logistf, brglm2) alongside the
zero-truncated intensity from this package.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.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.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().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).The estimators are hardened for the difficult likelihoods this package targets (near-boundary dispersion, zero-heavy and dummy-heavy panels):
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.peacekeeping dataset (UN peacekeeping
contributions, a state-year roster with structural zeros).broom tidy()/glance() methods
for all model classes (augment() for cpb), 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.