Computes confidence intervals of parameters for bias-reduced estimation
Computes confidence intervals for one or more parameters when
estimation is performed using brglm. The resulting confidence
intervals are based on manipulation of the profiles of the deviance,
the penalized deviance and the modified score statistic (see
profileObjectives).
## S3 method for class 'brglm'
confint(object, parm = 1:length(coef(object)), level = 0.95,
verbose = TRUE, endpoint.tolerance = 0.001,
max.zoom = 100, zero.bound = 1e-08, stepsize = 0.5,
stdn = 5, gridsize = 10, scale = FALSE, method = "smooth",
ci.method = "union", n.interpolations = 100, ...)
## S3 method for class 'profile.brglm'
confint(object, parm, level = 0.95, method = "smooth",
ci.method = "union", endpoint.tolerance = 0.001,
max.zoom = 100, n.interpolations = 100, verbose = TRUE,
...)object |
an object of class |
parm |
either a numeric vector of indices or a character vector
of names, specifying the parameters for which confidence intervals
are to be estimated. The default is all parameters in the fitted
model. When |
level |
the confidence level required. The default is 0.95. When
|
verbose |
logical. If |
endpoint.tolerance |
as in |
max.zoom |
as in |
zero.bound |
as in |
stepsize |
as in |
stdn |
as in |
gridsize |
as in |
scale |
as in |
method |
as in |
ci.method |
The method to be used for the construction of
confidence intervals. It can take values |
n.interpolations |
as in |
... |
further arguments to or from other methods. |
In the case of logistic regression Heinze & Schemper (2002) and Bull et. al. (2007) suggest the use of confidence intervals based on the profiles of the penalized likelihood, when estimation is performed using maximum penalized likelihood.
Kosmidis (2007) illustrated that because of the shape of the penalized likelihood, confidence intervals based on the penalized likelihood could exhibit low or even zero coverage for hypothesis testing on large parameter values and also misbehave illustrating severe oscillation (see Brown et. al., 2001); see, also Kosmidis & Firth (2021) for discussion on the schrinkage implied by bias reduction and what that entails for inference. Kosmidis (2007) suggested an alternative confidence interval that is based on the union of the confidence intervals resulted by profiling the ordinary deviance for the maximum likelihood fit and by profiling the penalized deviance for the maximum penalized fit. Such confidence intervals, despite of being slightly conservative, illustrate less oscillation and avoid the loss of coverage. Another possibility is to use the mean of the corresponding endpoints instead of “union”. Yet unpublished simulation studies suggest that such confidence intervals are not as conservative as the “union” based intervals but illustrate more oscillation, which however is not as severe as in the case of the penalized likelihood based ones.
The properties of the “union” and “mean” confidence
intervals extend to all the links that are supported by
brglm, when estimation is performed using maximum
penalized likelihood.
In the case of estimation using modified scores and for models other
than logistic, where there is not an objective that is maximized, the
profiles of the penalized likelihood for the construction of the
“union” and “mean” confidence intervals can be replaced
by the profiles of modified score statistic (see
profileObjectives).
The confint method for brglm and profile.brglm
objects implements the “union” and “mean” confidence
intervals. The method is chosen through the ci.method argument.
A matrix with columns the endpoints of the confidence intervals for the specified (or profiled) parameters.
Ioannis Kosmidis, ioannis.kosmidis@warwick.ac.uk
Kosmidis I. and Firth D. (2021). Jeffreys-prior penalty, finiteness and shrinkage in binomial-response generalized linear models. Biometrika, 108, 71–82.
Brown, L. D., Cai, T. T. and DasGupta, A. (2001). Interval estimation for a binomial proportion (with discussion). Statistical Science 16, 101–117.
Bull, S. B., Lewinger, J. B. and Lee, S. S. F. (2007). Confidence intervals for multinomial logistic regression in sparse data. Statistics in Medicine 26, 903–918.
Heinze, G. and Schemper, M. (2002). A solution to the problem of separation in logistic regression. Statistics in Medicine 21, 2409–2419.
Kosmidis, I. (2007). Bias reduction in exponential family nonlinear models. PhD Thesis, Department of Statistics, University of Warwick.
## Begin Example 1
## Not run:
library(MASS)
data(bacteria)
contrasts(bacteria$trt) <- structure(contr.sdif(3),
dimnames = list(NULL, c("drug", "encourage")))
# fixed effects analyses
m.glm.logit <- brglm(y ~ trt * week, family = binomial,
data = bacteria, method = "glm.fit")
m.brglm.logit <- brglm(y ~ trt * week, family = binomial,
data = bacteria, method = "brglm.fit")
p.glm.logit <- profile(m.glm.logit)
p.brglm.logit <- profile(m.brglm.logit)
#
plot(p.glm.logit)
plot(p.brglm.logit)
# confidence intervals for the glm fit based on the profiles of the
# ordinary deviance
confint(p.glm.logit)
# confidence intervals for the brglm fit
confint(p.brglm.logit, ci.method = "union")
confint(p.brglm.logit, ci.method = "mean")
# A cloglog link
m.brglm.cloglog <- update(m.brglm.logit, family = binomial(cloglog))
p.brglm.cloglog <- profile(m.brglm.cloglog)
plot(p.brglm.cloglog)
confint(m.brglm.cloglog, ci.method = "union")
confint(m.brglm.cloglog, ci.method = "mean")
## End example
## End(Not run)
## Not run:
## Begin Example 2
y <- c(1, 1, 0, 0)
totals <- c(2, 2, 2, 2)
x1 <- c(1, 0, 1, 0)
x2 <- c(1, 1, 0, 0)
m1 <- brglm(y/totals ~ x1 + x2, weights = totals,
family = binomial(cloglog))
p.m1 <- profile(m1)
confint(p.m1, method="zoom")
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.