paired.boot: Paired Bootstrap in Linear Models
In lmboot: Bootstrap in Linear Models

Description Usage Arguments Details Value Author(s) References Examples

This function performs the paired bootstrap in linear models as described by Efron (1979, ISBN:978-1-4612-4380-9). Linear models incorporating categorical and/or quantitative predictor variables with a quantitative response are allowed. The function output creates the bootstrap sampling distribution for each coefficient. Estimation is performed via least squares.

1	paired.boot(formula, B = 1000, seed = NULL, data = NULL)

`formula`	input a linear model formula of the form `response`~`predictors` as you would in the `lm()` function. All variables must contain non-missing entries.
`B`	number of bootstrap samples. This should be a large, positive integer value.
`seed`	optionally, set a value for the seed for the bootstrap sample generation. The default `NULL` will pick a random value for the seed.
`data`	optionally, input the name of the dataset where variables appearing in the model are stored.

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.

`bootEstParam`	matrix containing the bootstrap parameter estimates. Each column corresponds to a coefficient. There are `B` rows, each corresponding to a bootstrap sample.
`origEstParam`	vector containing the least squares parameter estimates. These are the same as estimates obtained from `lm`.
`seed`	numerical value set for the seed. This is associated with the set of bootstrap parameter estimates and helps the process to be reproducible.

Megan Heyman, heyman@rose-hulman.edu

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

Seed <- 14
set.seed(Seed)
y <- rnorm(20) #randomly generated response
x <- rnorm(20) #randomly generated predictor
PairObj <- paired.boot(y~x, B=100, seed=Seed) #perform the paired bootstrap

#plot the sampling distribution of the slope coefficient
hist(PairObj$bootEstParam[,2], main="Paired Bootstrap Sampling Distn.",
     xlab="Slope Estimate") 

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