Auxiliary function for glm fitting using the brglmFit method.
Typically only used internally by brglmFit, but may
be used to construct a control argument.
brglmControl(
epsilon = 1e-06,
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 = 1e-06,
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
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 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
Jeffreys-prior penalty. See, Kosmidis & Firth (2020) 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.
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, Kenne Pagui E C, Sartori N (2020). Mean and median bias reduction in generalized linear models. *Statistics and Computing*, **30**, 43-59 doi: 10.1007/s11222-019-09860-6
Kosmidis I, Firth D (2020). Jeffreys-prior penalty, finiteness and shrinkage in binomial-response generalized linear models. *Biometrika* doi: 10.1093/biomet/asaa052
Firth D (1993). Bias reduction of maximum likelihood estimates. Biometrika, **80**, 27-38 doi: 10.2307/2336755
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")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.