bootlm: Nonparametric Bootstrapping of Heteroskedastic Linear Regression Models

Description

Generates $B$ nonparametric bootstrap replications of a linear regression model that may have heteroskedasticity.

Usage

bootlm(
  object,
  sampmethod = c("pairs", "wild"),
  B = 1000L,
  resfunc = c("identity", "hccme"),
  fastfit = TRUE,
  ...
)

Value

A list object of class "bootlm", containing B objects, each of which is a bootstrapped linear regression model fit by Ordinary Least Squares. If fastfit was set to TRUE, each of these objects will be a list containing named objects y (the bootstrap response vector), X (the bootstrap design matrix, which is just the original design matrix under the wild bootstrap), e (the residual vector from the Ordinary Least Squares fit to this bootstrap data set), beta.hat (the vector of coefficient estimates from the Ordinary Least Squares fit to this bootstrap data set),

sampmethod, and ind (a vector of the indices from the original data set used in this bootstrap sample; ignored under the wild bootstrap) of the kind returned by

lm.fit; otherwise, each will be an object of class

"lm".

Arguments

object: Either an object of class "lm" (generated by lm), an object of class "alvm.fit" (generated by alvm.fit), or an object of class "anlvm.fit" (generated by anlvm.fit)
sampmethod: A character, either "pairs" or "wild", indicating the method to be used to generate the resampled models: bootstrapping pairs Efron93skedastic or the wild bootstrap Davidson08skedastic. Defaults to "pairs".
B: An integer representing the number of bootstrapped linear regression models to generate; defaults to 1000L
resfunc: Either a character naming a function to call to apply a transformation to the Ordinary Least Squares residuals, or a function to apply for the same purpose. This argument is ignored if sampmethod is "pairs". The only two character values accepted are "identity", in which case no transformation is applied to the residuals, and "hccme", in which case the transformation corresponds to a heteroskedasticity-consistent covariance matrix estimator calculated from hccme. If resfunc is a function, it is assumed that its first argument is the numeric vector of residuals.
fastfit: A logical indicating whether the lm.fit function should be used to fit the bootstrapped regression models for greater computational speed; defaults to TRUE. This affects the class of the returned value (see below). If FALSE, lm is used to fit the bootstrapped regression models.
...: Other arguments to pass to hccme

Details

Each replication of the pairs bootstrap entails drawing a sample of size $n$ (the number of observations) with replacement from the indices $i=1,2,\ldots,n$. The pair or case $(y_i, X_i)$ is included as an observation in the bootstrapped data set for each sampled index. An Ordinary Least Squares fit to the bootstrapped data set is then computed.

Under the wild bootstrap, each replication of the linear regression model is generated by first independently drawing $n$ random values $r_i$, $i=1,2,\ldots,n$, from a distribution with zero mean and unit variance. The $i$th bootstrap response is then computed as $$X_i'\hat{\beta} + f_i(e_i) r_i$$, where $X_i$ is the $i$th design observation, $\hat{\beta}$ is the Ordinary Least Squares estimate of the coefficient vector $\beta$, $e_i$ is the $i$th Ordinary Least Squares residual, and $f_i(\cdot)$ is a function performing some transformation on the residual. An Ordinary Least Squares fit is then computed on the original design matrix and the bootstrap response vector.

References

Examples

Run this code

mtcars_lm <- lm(mpg ~ wt + qsec + am, data = mtcars)
mybootlm <- bootlm(mtcars_lm)

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