This function provides a simple front-end to the
boot function in the
boot package that is tailored to bootstrapping based on regression models. Whereas
boot is very general and therefore
has many arguments, the
Boot function has very few arguments.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Boot(object, f=coef, labels=names(f(object)), R=999, method=c("case", "residual"), ncores=1, ...) ## Default S3 method: Boot(object, f=coef, labels=names(f(object)), R=999, method=c("case", "residual"), ncores=1, start = FALSE, ...) ## S3 method for class 'lm' Boot(object, f=coef, labels=names(f(object)), R=999, method=c("case", "residual"), ncores=1, ...) ## S3 method for class 'glm' Boot(object, f=coef, labels=names(f(object)), R=999, method=c("case", "residual"), ncores=1, ...) ## S3 method for class 'nls' Boot(object, f=coef, labels=names(f(object)), R=999, method=c("case", "residual"), ncores=1, ...)
A regression object of class
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
Provides labels for the statistics computed by
Number of bootstrap samples. The number of bootstrap samples actually computed may be smaller than this value if either the fitting method is iterative and fails to converge for some boothstrap samples, or if the rank of a fitted model is different in a bootstrap replication than in the original data.
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
Arguments passed to the
Should the estimates returned by
A numeric argument that specifies the number of cores for parallel processing. If less than or equal to 1, no parallel processing wiill be used.
Boot uses a
regression object and the choice of
method, and creates a function that is
passed as the
statistic argument to the
boot function in the boot package. The argument
R is also passed to
ncores is greater than 1, then the
ncpus arguments to
boot are set appropriately to use multiple codes, if available, on your computer. All other arguments to
boot are kept at their default values unless you pass values for them.
The methods available for
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
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
For the default object to work with other types of regression models, 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 which will effectively ignore setting the hatvalues. In addition, the
data argument should contain no missing values among the columns actually used in fitting the model, as the resampling may incorrectly attempt to include cases with missing values. For
nls, missing values are handled correctly.
An attempt to fit using a bootstrap sample may fail. In a
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
The summary methods handle the
Fox and Weisberg (2017) cited below discusses this function and provides more examples.
boot for the returned value of the structure returned by this function.
Sanford Weisberg, [email protected]. Achim Zeileis added multicore support, and also fixed the default method to work for many more regression models.
Davison, A, and Hinkley, D. (1997) Bootstrap Methods and their Applications. Oxford: Oxford University Press.
Fox, J. and Weisberg, S. (2019) Companion to Applied Regression, Third Edition. Thousand Oaks: Sage.
Fox, J. and Weisberg, S. (2017) 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.
1 2 3 4 5 6 7 8 9
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)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.