# Boot

##### Bootstrapping for regression models

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.

- Keywords
- regression

##### Usage

`Boot(object, f=coef, labels=names(f(object)), R=999, method=c("case", "residual"), …)`# S3 method for default
Boot(object, f=coef, labels=names(f(object)),
R=999, method=c("case", "residual"), start = FALSE, …)

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

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

# S3 method for nls
Boot(object, f=coef, labels=names(f(object)),
R=999, method=c("case", "residual"), …)

##### Arguments

- object
A regression object of class

`lm`

,`glm`

or`nls`

. The function may work with other regression objects that support the`update`

method and have a`subset`

argument- f
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,`f = function(obj) coef(obj)[1]/coef(obj[2]`

will bootstrap the ratio of the first and second coefficient estimates.- labels
Provides labels for the statistics computed by

`f`

. If this argument is of the wrong length, then generic labels will be generated.- R
Number of bootstrap samples. The number of bootstrap samples actually computed may be smaller than this value if either the fitting method is iterative, or if the rank of a fittle

`lm`

or`glm`

model is different in the bootstrap replication than in the original data.- 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`

and`nls`

objects and will return an error for`glm`

objects.- …
Arguments passed to methods. The default method passes these on to the

`boot`

function.- start
Should the

`f`

paramters be passed as`start`

values to the`update`

in each bootstrap iteration? Alternatively,`start`

can also be a numeric vector that is passed to the`update`

.

##### 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`

and `nls`

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). For `nls`

objects ordinary residuals are used
in the resampling rather than the standardized residuals used in the `lm`

method. 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`

.

For the default object to work with other types of regression model, the model must have methods for the the following generic functions: `residuals(object, type="pearson")`

must return Pearson residuals; `fitted(object)`

must return fitted values; `hatvalues(object)`

should return the leverages, or perhaps the value 1.

An attempt to model fit to a bootstrap sample may fail. In a `lm`

or
`glm`

fit, the bootstrap sample could have a different rank from the original
fit. In an `nls`

fit, convergence may not be obtained for some bootstraps.
In either case, `NA`

are returned for the value of the function `f`

.
The summary methods handle the `NA`

s appropriately.

##### Value

See `boot`

for the returned value from this function. The car
package includes additional generic functions `summary`

, `vcov.boot`

, `confint.boot`

and `hist.boot`

that work
with boot objects.

##### 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.

Weisberg, S. (2014) *Applied Linear Regression*, Fourth Edition, Wiley
Wiley, Chapters 4 and 11.

##### See Also

Functions that work with
`Boot`

objects from the `boot`

package are
`boot.array`

,
`boot.ci`

,
`plot.boot`

and
`empinf`

. Additional
functions in the `car`

package are
`summary.boot`

,
`confint.boot`

, and
`hist.boot`

.

##### Examples

```
# NOT RUN {
m1 <- lm(Fertility ~ ., swiss)
betahat.boot <- Boot(m1, R=199) # 199 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=199, f=sigmaHat, labels="sigmaHat")
summary(sigmahat.boot)
confint(sigmahat.boot)
# }
```

*Documentation reproduced from package car, version 2.1-6, License: GPL (>= 2)*