R: Bootstrapping for regression models

Boot {car} | R Documentation

## 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

    ## Default S3 method:
    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"))

    ## S3 method for class 'nls'
    Boot(object, f=coef, labels=names(coef(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.

### 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`.

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, confint and hist that works with boot objects.

### Author(s)

Sanford Weisberg, sandy@umn.edu.

### 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

    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)

[Package car version 2.1-4 Index]