brglm (version 0.5-2)

confint.brglm: Computes confidence intervals of parameters for bias-reduced estimation

Description

Computes confidence intervals for one or more parameters when estimation is performed using brglm. The resultant confidence intervals are based on manipulation of the profiles of the deviance, the penalized deviance and the modified score statistic (see profileObjectives).

Usage

## 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,
        ...)

Arguments

object

an object of class "brglm" or "profile.brglm".

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 object is of class "pro

level

the confidence level required. The default is 0.95. When object is of class "profile.brglm", level is not used and the level attribute of object is used instead.

verbose

logical. If TRUE (default) progress indicators are printed during the progress of calculating the confidence intervals.

endpoint.tolerance

as in confintModel.

max.zoom

as in confintModel.

zero.bound

as in confintModel.

stepsize

as in confintModel.

stdn

as in confintModel.

gridsize

as in confintModel.

scale

as in confintModel.

method

as in confintModel.

ci.method

The method to be used for the construction of confidence intervals. It can take values "union" (default) and "mean" (see Details).

n.interpolations

as in confintModel.

...

further arguments to or from other methods.

Value

• A matrix with columns the endpoints of the confidence intervals for the specified (or profiled) parameters.

Details

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). 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.

References

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.

See Also

confintModel, profileModel, profile.brglm.

Examples

## Begin Example 1
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
## 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")