brglmControl
provides default values and
sanity checking for the various constants that control the
iteration and generally the behaviour of
brglmFit
.
When trace
is true, calls to cat
produce the
output for each iteration. Hence, options(digits = *)
can be used to increase the precision.
transformation
sets the transformation of the
dispersion parameter for which the bias reduced estimates are
computed. Can be one of "identity", "sqrt", "inverse", "log"
and "inverseSqrt". Custom transformations are accommodated by
supplying a list of two expressions (transformation and
inverse transformation). See the examples for more details.
The value of response_adjustment
is only relevant if
brglmFit
is called with start = NULL
, and
family
is binomial
or
poisson
. For those models, an initial maximum
likelihood fit is obtained on adjusted data to provide
starting values for the iteration in brglmFit
. The
value of response_adjustment
governs how the data is
adjusted. Specifically, if family
is binomial
,
then the responses and totals are adjusted by and 2 *
response_adjustment
, respectively; if family
is
poisson
, then the responses are adjusted by and
response_adjustment
. response_adjustment = NULL
(default) is equivalent to setting it to
"number of parameters"/"number of observations".
. . When type = "AS_mixed"
(default), mean bias reduction is
used for the regression parameters, and median bias reduction
for the dispersion parameter, if that is not fixed. This
adjustment has been developed based on equivariance arguments
(see, Kosmidis et al, 2019, Section 4) in order to produce
regression parameter estimates that are invariant to arbitrary
contrasts, and estimates for the dispersion parameter that are
invariant to arbitrary non-linear transformations. type =
"AS_mixed"
and type = "AS_mean"
return the same results
if brglmFit
is called with family
binomial
or poisson
(i.e. families with fixed dispersion).
When type = "MPL_Jeffreys"
, brglmFit
will
maximize the penalized log-likelihood
$$l(\beta, \phi) + a\log \det i(\beta, \phi)$$ where \(i(\beta, \phi)\)
is the expected information matrix about the regression
parameters \(\beta\) and the dispersion parameter
\(\phi\). See, vignette("iteration", "brglm2")
for more
information. The argument $a$ controls the amount of
penalization and its default value is a = 1/2
,
corresponding to maximum penalized likelihood using a
Jeffreys-prior penalty. See, Kosmidis & Firth (2019) for
proofs and discussion about the finiteness and shrinkage
properties of the maximum penalized likelihood estimators for
binomial-response generalized linear models.
The estimates from type = "AS_mean"
and type =
"MPL_Jeffreys"
with a = 1/2
(default) are identical
for Poisson log-linear models and logistic regression models,
i.e. for binomial and Poisson regression models with canonical
links. See, Firth (1993) for details.
brglm_control
is an alias to brglmControl
.