Bootstrapping

Bootstrapping is a method for deriving robust estimates of standard errors and confidence intervals for estimates such as the mean, median, proportion, odds ratio, correlation coefficient or regression coefficient. It may also be used for constructing hypothesis tests. Bootstrapping is most useful as an alternative to parametric estimates when the assumptions of those methods are in doubt (as in the case of regression models with heteroscedastic residuals fit to small samples), or where parametric inference is impossible or requires very complicated formulas for the calculation of standard errors (as in the case of computing confidence intervals for the median, quartiles, and other percentiles).

Examples. A telecommunications firm loses about 27% of its customers to churn each month. In order to properly focus churn reduction efforts, management wants to know if this percentage varies across predefined customer groups. Using bootstrapping, you can determine whether a single rate of churn adequately describes the four major customer types.

In a review of employee records, management is interested in the previous work experience of employees. Work experience is right skewed, which makes the mean a less desirable estimate of the "typical" previous work experience among employees than the median. However, parametric confidence intervals are not available for the median in the product.

Management is also interested in determining what factors are associated with employee salary increases by fitting a linear model to the difference between current and starting salaries. When bootstrapping a linear model, you can use special resampling methods (residual and wild bootstrap) to obtain more accurate results.

Many procedures support bootstrap sampling and pooling of results from analysis of bootstrap samples. Controls for specifying bootstrap analyses are integrated directly as a common subdialog in procedures that support bootstrapping. Settings on the bootstrap dialog persist across procedures so that if you run a Frequencies analysis with bootstrapping through the dialogs, bootstrapping will be turned on by default for other procedures that support it.

To Obtain a Bootstrap Analysis

1. From the menus choose a procedure that supports bootstrapping and click Bootstrap.
2. Select Perform bootstrapping.

Optionally, you can control the following options:

Number of samples. For the percentile and BCa intervals produced, it is recommended to use at least 1000 bootstrap samples. Specify a positive integer.

Set seed for Mersenne Twister. Setting a seed allows you to replicate analyses. Using this control is similar to setting the Mersenne Twister as the active generator and specifying a fixed starting point on the Random Number Generators dialog, with the important difference that setting the seed in this dialog will preserve the current state of the random number generator and restore that state after the analysis is complete. See the topic Random Number Generators for more information.

Confidence Intervals. Specify a confidence level greater than 50 and less than 100. Percentile intervals simply use the ordered bootstrap values corresponding to the confidence interval percentiles. For example, a 95% percentile confidence interval uses the 2.5th and 97.5th percentiles of the bootstrap values as the lower and upper bounds of the interval (interpolating the bootstrap values if necessary). Bias corrected and accelerated (BCa) intervals are adjusted intervals that are more accurate at the cost of requiring more time to compute.

Sampling. The Simple method is case resampling with replacement from the original dataset. The Stratified method is case resampling with replacement from the original dataset, within the strata defined by the cross-classification of strata variables. Stratified bootstrap sampling can be useful when units within strata are relatively homogeneous while units across strata are very different.

Performing bootstrapping pastes BOOTSTRAP command syntax.