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gls_mult() for feasible generalized least squares
estimation under multiplicative heteroskedasticity. The
estimator argument chooses the fit, either
"ml" (default, Gaussian maximum likelihood) or
"two_step" (Harvey’s corrected auxiliary regression), and
for maximum likelihood the method argument selects the
stats::optim() algorithm: "BFGS" (default),
"Nelder-Mead", "CG", or
"L-BFGS-B". New coef() and vcov()
methods access the mean and dispersion coefficients via
model =, and confint(), tests(),
summary(), print(), fitted(), and
residuals() methods support applied inference, while
logLik() and nobs() enable AIC()
and BIC() for maximum likelihood fits. The package
Description now also covers feasible generalized least
squares following Harvey (1976) and Cribari-Neto and Pereira
(2019).vcov_hc()
and hcinfer() compute
g_t = (1 - h_t)^(-delta_t / 2) instead of the expression
g_t = (1 - h_t)^(-delta_t) printed in Section 3 of the
original article, keeping
delta_t = min(h_t / h_bar, max(4, k * h_max / h_bar)) and
the default k = 0.7 unchanged. HC5 adjustment factors are
therefore smaller, and HC5 standard errors, Wald statistics, p-values,
and confidence intervals differ from those returned by earlier versions.
HC5m is unaffected because it follows Li, Zhang, Zhang and Wang (2016)
and applies its own exponent without the factor 1/2, so
type = "hc5m" with k1 = 0,
k2 = 0, and k3 = 1 no longer reproduces
type = "hc5" and instead squares its adjustment
factor.vcov_hc() help page and in the methodology vignette, and
added the 2008 erratum to the references of hcinfer(),
vcov_hc(), tests(), the methodology vignette,
and the package Description.boot_pairs() for pairs (case) bootstrap standard
errors and confidence intervals of ordinary least squares coefficients.
It resamples the observations with replacement, refits the model on each
replicate, and summarizes the sampling distribution of the coefficients,
providing an assumption-free empirical reference for the analytic
heteroskedasticity-consistent standard errors from
hcinfer() and vcov_hc(). Percentile, basic,
and normal intervals are available, the resampling is reproducible
through the seed argument, and the replicate fits can
optionally run in parallel via purrr::in_parallel() and
mirai without changing the numeric result.coef(), vcov(),
confint(), print(), and plot()
methods for the hcinfer_boot objects returned by
boot_pairs(). vcov() returns the bootstrap
covariance matrix of the coefficients, confint() can
recompute intervals at a different level or
type directly from the stored replicates, and
plot() draws the bootstrap confidence intervals, coloring
each coefficient by whether its interval excludes or includes zero.hcinfer() and vcov_hc() now accept
independent HCbeta shape caps from 50 through 25000 inclusive, with
defaults of 10000. HC0, HC1, and HCbeta also remain defined for an exact
leverage value of one, while HC2, HC3, HC4, HC4m, HC5, and HC5m retain
the positive leverage-complement requirement.hcinfer() and vcov_hc() now enforce the
fixed HCbeta shape floor of 0.01 after shrinkage and before the upper
caps, including for nondefault leverage-complement truncation limits.
The shape floor remains fixed when lower changes and is not
a method argument.PublicSchools2 dataset with 2024 per capita
income, 2025 public school expenditure per student, a Southern-region
indicator, and complete variable and source documentation.PublicSchools
from Washington DC to
District of Columbia.plot() now supports vcov_hc() objects,
producing leverage-versus-adjustment-factor graphics for inspecting the
relationship between h_t and g_t.tests() as a formal extractor for
coefficient-level Wald test results. The function mirrors the API of
confint(): an optional parm argument selects
coefficients by name or position, and an optional alpha
argument recomputes the reject column without affecting the
stored p-values or test statistics.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.