brlr {brlr} | R Documentation |
Fits a logistic regression by maximum penalized likelihood, in which the penalty function is the Jeffreys invariant prior. This removes the O(1/n) term from the asymptotic bias of estimated coefficients (Firth, 1993), and always yields finite estimates and standard errors (whereas the MLE is infinite in situations of complete or quasi-complete separation).
brlr(formula, data = NULL, offset, weights, start, ..., subset, dispersion = 1, na.action = na.omit, contrasts = NULL, x = FALSE, br = TRUE, control = list(maxit = 200))
formula |
a model formula as for glm , or an
object of class glm |
data |
an data frame as for glm |
offset |
an optional vector as for glm |
weights |
an optional vector as for glm |
start |
an optional set of starting values (of the model coefficients) for the optimization |
... |
further arguments passed to or from other methods |
subset |
an optional vector specifying a subset of observations to be used in the fitting process |
dispersion |
an optional parameter for over- or under-dispersion relative to binomial variation – default is 1 |
na.action |
a function which indicates what should happen when the data
contain `NA's. The default is set by the na.action setting
of options , and is na.fail if that is unset. The
``factory-fresh'' default is na.omit . |
contrasts |
an optional list. See the contrasts.arg of
model.matrix.default . |
x |
should the model matrix be included in the resultant object? |
br |
a logical switch indicating whether the bias-reducing
penalty is applied; default is TRUE |
control |
as for optim |
brlr
has essentially the same user interface as
glm(family=binomial, ...)
—
see the example below.
A model object of class brlr
, with components
coefficients |
as for glm |
deviance |
as for glm |
penalized.deviance |
deviance minus 2*logdet(Fisher information) |
fitted.values |
as for glm |
linear.predictors |
as for glm |
call |
as for glm |
formula |
as for glm |
convergence |
logical, did the optimization converge? |
niter |
number of iterations of the optimization algorithm
(BFGS via optim ) |
df.residual |
as for glm |
df.null |
as for glm |
model |
as for glm |
y |
the observed binomial proportions, as for glm |
family |
a family object, binomial with logistic link,
as for glm |
offset |
as for glm |
prior.weights |
as for glm |
terms |
as for glm |
dispersion |
as for glm ; the
dispersion argument if supplied, otherwise 1 |
bias.reduction |
logical, the value of argument br |
leverages |
the diagonal elements of the model's ``hat'' matrix |
qr |
as for glm |
rank |
as for glm |
FisherInfo |
the estimated Fisher information matrix |
contrasts |
as for glm |
xlevels |
as for glm |
residuals |
as for glm |
data |
as for glm |
boundary |
as for glm ; but always FALSE |
x |
if x = TRUE is specified |
control |
the control list as used in the call to
optim |
1. Methods specific to the brlr
class of models are
print.brlr
summary.brlr
print.summary.brlr
vcov.brlr
add1.brlr
drop1.brlr
Others are inherited from the glm
class.
2. The results of the bias-reduced fit typically have regression coefficients slightly closer to zero than the maximum likelihood estimates, and slightly smaller standard errors. (In logistic regression, bias reduction is achieved by a slight shrinkage of coefficients towards zero; thus bias reduction also reduces variance.) The difference is typically small except in situations of sparse data and/or complete separation. See also Heinze and Schemper (2002), Zorn (2005).
David Firth, d.firth@warwick.ac.uk
Firth, D. (1993) Bias reduction of maximum likelihood estimates. Biometrika 80, 27–38.
Firth, D. (1992) Bias reduction, the Jeffreys prior and GLIM. In Advances in GLIM and Statistical Modelling, Eds. L Fahrmeir, B J Francis, R Gilchrist and G Tutz, pp91–100. New York: Springer.
Heinze, G. and Schemper, M. (2002) A solution to the problem of separation in logistic regression. Statistics in Medicine 21, 2409–2419.
Zorn, C (2005). A solution to separation in binary response models. Political Analysis 13, 157–170.
## Habitat preferences of lizards, from McCullagh and Nelder (1989, p129); ## this reproduces the results given in Firth (1992). ## ## First the standard maximum-likelihood fit: data(lizards) glm(cbind(grahami, opalinus) ~ height + diameter + light + time, family = binomial, data=lizards) ## Now the bias-reduced version: brlr(cbind(grahami, opalinus) ~ height + diameter + light + time, data=lizards)