Boot: Bootstrapping for regression models

Description

This function provides a simple front-end to the boot function in the package also called boot. Whereas boot is very general and therefore has many arguments, the Boot function has very few arguments, but should meet the needs of many users.

Usage

## S3 method for class 'default':
Boot(object, f=coef, labels=names(coef(object)),
                     R=999, method=c("case", "residual"))
                     
## S3 method for class 'lm':
Boot(object, f=coef, labels=names(coef(object)),
                     R=999, method=c("case", "residual"))

## S3 method for class 'glm':
Boot(object, f=coef, labels=names(coef(object)),
                     R=999, method=c("case", "residual"))

Arguments

object

A regression object of class lm or glm. The function may work with other regression objects that support the update method and have a subset argument, but it will fail if the fitting method for the mod

A function whose one argument is the name of a regression object that will be applied to the updated regression object to compute the statistics of interest. The default is coef, to return to regression coefficient estimates. For example,

labels

Provides labels for the statistics computed by f. If this argument is of the wrong length, then generic labels will be generated.

Number of bootstrap samples.

method

The bootstrap method, either case for resampling cases or residuals for a residual bootstrap. See the details below. The residual bootstrap is available only for lm objects and will return an error for

Value

See boot for the returned value from this function. The car package includes additional generic functions, as listed below.

Details

Whereas the boot function is very general, Boot is very specific. It takes the information from a regression object and the choice of method, and creates a function that is passed as the statistic argument to boot. The argument R is also passed to boot. All other arguments to boot are kept at their default values. The methods available for lm objects are case and residual. The case bootstrap resamples from the joint distribution of the terms in the model and the response. The residual bootstrap fixes the fitted values from the original data, and creates bootstraps by adding a bootstrap sample of the residuals to the fitted values to get a bootstrap response. It is an implementation of Algorithm 6.3, page 271, of Davison and Hinkley (1997). The residual bootstrap for generalized linear models has several competing approaches, but none are without problems. If you want to do a residual bootstrap for a glm, you will need to write your own call to boot. This function may fail if the model fit to any of the bootstrap samples is of lower rank than the model fit to the original data. This will occur, for example, if the model includes factors and interactions with a very small number of observations per cell. In this case bootstrap samples may have zero counts in some cells and lose rank.

References

Davison, A, and Hinkley, D. (1997) Bootstrap Methods and their Applications. Oxford: Oxford University Press. Fox, J. and Weisberg, S. (2011) Companion to Applied Regression, Second Edition. Thousand Oaks: Sage. Fox, J. and Weisberg, S. (2012) Bootstrapping, http://socserv.mcmaster.ca/jfox/Books/Companion/appendix/Appendix-Bootstrapping.pdf. S. Weisberg (2005) Applied Linear Regression, Third Edition. Wiley, Chapters 4 and 11.

Examples

Run this code

m1 <- lm(Fertility ~ ., swiss)
betahat.boot <- Boot(m1, R=99) # 99 bootstrap samples--too small to be useful
summary(betahat.boot)  # default summary
confint(betahat.boot)
hist(betahat.boot)
# Bootstrap for the estimated residual standard deviation:
sigmahat.boot <- Boot(m1, R=99, f=sigmaHat, labels="sigmaHat")
summary(sigmahat.boot)
confint(sigmahat.boot)

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