Bootstrapping with Models for Count Data

Abstract

Two methods of bootstrap resampling are discussed with log-linear models for count data. The first involves the resampling of observations and the second involves the resampling of Pearson residuals taking into account changes in the distribution of residuals associated with the expected values of counts. The use of both methods is illustrated on two data sets; one data set concerns the number of ear infections of swimmers related to whether they are frequent swimmers or not and three other variables, and the other data set concerns the number of visits to a doctor made in the last 2 weeks related to the age of subjects and 10 other variables. A third data set on the number of marine mammal interactions in different years and fishing areas is also used as an example. In this case only the second bootstrap method can be used because the nature of the data allows the bootstrap resampling of observations to produce sets of data that could not have occurred in practice. Simulation results indicate that the bootstrap results are slightly better than the results from a conventional analysis for the first data set, and much better than the results from a conventional analysis for the second data set, but a conventional analysis works well for the third data set while there are problems with bootstrap analyses.

Key Words:

• Bootstrap resampling
• Computer-intensive methods
• Generalized linear models
• Log-linear models

Notes

Note. Values shown are the regression coefficient estimates from the original data (Est), the estimated standard errors (Std Err) of the estimates from the conventional analysis and the estimated values from the two bootstrap resampling methods, and the significance (Signif) of the t-values based on the t-tables and the two bootstrap resampling methods.

Note. Values shown are the regression estimates (Est), the estimated standard errors (Std Err) of the estimates from the conventional analysis and the estimated standard errors from the two bootstrap resampling methods, and the significance (Signif) of the t-values based on the t-tables and the two bootstrap resampling methods.

Note. Values shown are the regression estimates (Est), the estimated standard errors (Std Err) of the estimates from the conventional analysis and the second bootstrap resampling method, and the significance (Signif) of the t-values based on the t-tables and the bootstrap resampling.