lmboot-package: Bootstrap in Linear Models

In lmboot: Bootstrap in Linear Models

Description

Various efficient and robust bootstrap methods are implemented for linear models with least squares estimation. Functions within this package allow users to create bootstrap sampling distributions for model parameters, test hypotheses about parameters, and visualize the bootstrap sampling or null distributions. Methods implemented for linear models include the wild bootstrap by Wu (1986) <doi:10.1214/aos/1176350142>, the residual and paired bootstraps by Efron (1979, ISBN:978-1-4612-4380-9), the delete-1 jackknife by Quenouille (1956) <doi:10.2307/2332914>, and the Bayesian bootstrap by Rubin (1981) <doi:10.1214/aos/1176345338>.

Details

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This package is useful to users who wish to perform bootstrap in linear models. The package contains functions to create the sampling distributions for linear model parameters using either efficient or robust bootstrap methods.

As classified by Liu and Singh (1992), efficient bootstrap types include the residual bootstrap (residual.boot()). These types of bootstrap are useful when it is not reasonable to assume that errors come from a normal distribution, but you may make other classical assumptions: errors are independent, have mean 0, and have constant variance.

Robust bootstrap types include the paired bootstrap (paired.boot), wild bootstrap (wild.boot), and the jackknife (jackknife). These types of bootstrap are useful when it is not reasonable to assumet that errors have constant variance, but you may make other classical assumptions: errors are independent and have mean 0.

The package also contains a function for Bayesian bootstrap (bayesian.boot and a function to perform bootstrap in the ANOVA hypothesis test (ANOVA.boot). The ANOVA bootstrap function has options to use the wild or residual bootstrap techniques and has been tested to work in 2-way ANOVA. Its functionality allows K-way ANOVA, however those capabilities have not been fully tested.

Currently, the user must manipulate the output of the function to conduct hypothesis tests and create confidence intervals for the predictor coefficients. More convenient/streamlined output is expected in future package versions.

Author(s)

Megan Heyman [aut, cre]

Maintainer: Megan Heyman <[e-mail]>

References

Efron, B. (1979). "Bootstrap methods: Another look at the jackknife." Annals of Statistics. Vol. 7, pp.1-26.

Liu, R. Y. and Singh, K. (1992). "Efficiency and Robustness in Resampling." Annals of Statistics. Vol. 20, No. 1, pp.370-384.

Rubin, D. B. (1981). "The Bayesian Bootstrap." Annals of Statistics. Vol. 9, No. 1, pp.130-134.

Wu, C.F.J. (1986). "Jackknife, Bootstrap, and Other Resampling Methods in Regression Analysis." Annals of Statistics. Vol. 14, No. 4, pp.1261 - 1295.

Examples

Seed <- 14
set.seed(Seed)
y <- rnorm(20) #randomly generated response
x <- rnorm(20) #randomly generated predictor

ResidObj <- residual.boot(y~x, B=100, seed=Seed) #perform the residual bootstrap
WildObj <- wild.boot(y~x, B=100, seed=Seed) #perform the wild bootstrap

#residual bootstrap 95% CI for slope parameter (percentile method)
quantile(ResidObj$bootEstParam[,2], probs=c(.025, .975))

#bootstrap 95% CI for slope parameter (percentile method)
quantile(WildObj$bootEstParam[,2], probs=c(.025, .975))

lmboot documentation built on June 3, 2019, 5:03 p.m.