Description Usage Arguments Details Value Author(s) References See Also Examples
Typically only used internally by brglmFit
, but may
be used to construct a control
argument.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27  brglmControl(
epsilon = 1e06,
maxit = 100,
check_aliasing = TRUE,
trace = FALSE,
type = c("AS_mixed", "AS_mean", "AS_median", "correction", "MPL_Jeffreys", "ML"),
transformation = "identity",
slowit = 1,
response_adjustment = NULL,
max_step_factor = 12,
a = 1/2,
...
)
brglm_control(
epsilon = 1e06,
maxit = 100,
check_aliasing = TRUE,
trace = FALSE,
type = c("AS_mixed", "AS_mean", "AS_median", "correction", "MPL_Jeffreys", "ML"),
transformation = "identity",
slowit = 1,
response_adjustment = NULL,
max_step_factor = 12,
a = 1/2,
...
)

epsilon 
positive convergence tolerance epsilon. Default is

maxit 
integer giving the maximal number of iterations
allowed. Default is 
check_aliasing 
logical indicating where a QR decomposition
of the model matrix should be used to check for
aliasing. Default is 
trace 
logical indicating if output should be produced for
each iteration. Default is 
type 
the type of fitting method to be used. The options are

transformation 
the transformation of the dispersion to be
estimated. Default is 
slowit 
a positive real used as a multiplier for the
stepsize. The smaller it is the smaller the steps are. Default
is 
response_adjustment 
a (small) positive constant or a vector
of such. Default is 
max_step_factor 
the maximum number of step halving steps to
consider. Default is 
a 
power of the Jeffreys prior penalty. See Details. 
... 
further arguments passed to

brglmControl
provides default values and sanity
checking for the various constants that control the iteration and
generally the behaviour of brglmFit
.
When trace = TRUE
, calls to cat
produce the output
for each iteration. Hence, options(digits = *)
can be used
to increase the precision.
When check_aliasing = TRUE
(default), a QR decomposition of
the model matrix is computed to check for aliasing. If the model
matrix is known to be of full rank, then check_aliasing =
FALSE
avoids the extra computational overhead of an additional QR
decomposition, which can be substantial for large model
matrices. However, setting check_aliasing = FALSE
is tells
brglmFit
that the model matrix is full rank, and hard
to trace back errors will result if it is rank deficient.
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, 2020, 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
nonlinear 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 loglikelihood
l(beta, phi) + a log det i(beta, phi)
where
i(beta, phi) is the expected information
matrix about the regression parameters β and the
dispersion parameter φ. 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
Jeffreysprior penalty. See, Kosmidis & Firth (2021) for proofs and
discussion about the finiteness and shrinkage properties of the
maximum penalized likelihood estimators for binomialresponse
generalized linear models.
The estimates from type = "AS_mean"
and type =
"MPL_Jeffreys"
with a = 1/2
(default) are identical for
Poisson loglinear 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
.
a list with components named as the arguments, including
symbolic expressions for the dispersion transformation
(Trans
) and its inverse (inverseTrans
)
Ioannis Kosmidis ioannis.kosmidis@warwick.ac.uk
Kosmidis I, Firth D (2021). Jeffreysprior penalty, finiteness and shrinkage in binomialresponse generalized linear models. *Biometrika*, **108**, 7182 doi: 10.1093/biomet/asaa052
Kosmidis I, Kenne Pagui E C, Sartori N (2020). Mean and median bias reduction in generalized linear models. *Statistics and Computing*, **30**, 4359 doi: 10.1007/s11222019098606
Firth D (1993). Bias reduction of maximum likelihood estimates. Biometrika, **80**, 2738 doi: 10.2307/2336755
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  data("coalition", package = "brglm2")
## The maximum likelihood fit with log link
coalitionML < glm(duration ~ fract + numst2, family = Gamma, data = coalition)
## Bias reduced estimation of the dispersion parameter
coalitionBRi < glm(duration ~ fract + numst2, family = Gamma, data = coalition,
method = "brglmFit")
coef(coalitionBRi, model = "dispersion")
## Bias reduced estimation of log(dispersion)
coalitionBRl < glm(duration ~ fract + numst2, family = Gamma, data = coalition,
method = "brglmFit", transformation = "log")
coef(coalitionBRl, model = "dispersion")
## Just for illustration: Bias reduced estimation of dispersion^0.25
my_transformation < list(expression(dispersion^0.25), expression(transformed_dispersion^4))
coalitionBRc < update(coalitionBRi, transformation = my_transformation)
coef(coalitionBRc, model = "dispersion")

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