Regression Bootstrapping
Abstract
Bootstrapping is a nonparametric procedure for testing whether linear regression model estimates are significant by determining their standard errors using resampling.
Brief Description
SmartPLS uses bootstrapping to determine the significance of estimates from a linear regression model. Bootstrapping involves creating subsamples of randomly drawn observations from the original dataset (with replacement). The subsample is then used to estimate the linear regression model. This process is repeated until a large number of random subsamples have been created (e.g., 10,000).
The parameter estimates obtained from the subsamples are used to derive the 95% confidence intervals for significance testing. In addition, bootstrapping provides the standard errors for the estimates, which allow t-values to be calculated to assess the significance of each estimate.
Hair et al. (2022) explain bootstrapping in more detail.
Bootstrapping Settings in SmartPLS
Subsamples
Bootstrapping creates subsamples of observations randomly drawn from the original dataset (with replacement). The number of observations in each bootstrap subsample is identical to the number of observations in the original sample (SmartPLS also accounts for the smaller number of observations in the original sample if you use case-by-case deletion to handle missing values).
To ensure stability of results, the number of subsamples should be large. For an initial evaluation, it may be advisable to choose a smaller number of bootstrap subsamples (e.g., 1,000) to be randomly drawn and estimated with the PLS-SEM algorithm, as this requires less time. However, a large number of bootstrap subsamples (e.g., 10,000) should be used to produce the final results.
Note: Larger numbers of bootstrap subsamples increase the computing time
Do Parallel Processing
If selected, the bootstrapping algorithm will be run on multiple processors (if your computer has more than one core). As each subsample can be calculated individually, subsamples can be calculated in parallel. Using parallel computing will reduce the computation time.
Confidence Interval Method
Specifies the bootstrapping method used to estimate non-parametric confidence intervals. The following bootstrapping methods are available (for more details, see Hair et al., 2022):
- Percentile Bootstrap (default)
- Studentized Bootstrap
- Bias-Corrected and Accelerated (BCa) Bootstrap
By default, we recommend using the percentile bootstrap. If you have concerns about a non-normal bootstrap distribution, you can alternatively use bias-corrected and accelerated (BCa) bootstrapping.
Test Type
Specifies whether a one-tailed or two-tailed significance test is performed
Significance Level
Specifies the significance level of the test statistic.
References
- Hair, J. F., Hult, G. T. M., Ringle, C. M., and Sarstedt, M. (2022). A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM), 3rd Ed., Sage: Thousand Oaks.
- Davison, A. C., and Hinkley, D. V. (1997). Bootstrap Methods and Their Application, Cambridge University Press: Cambridge.
- Efron, B., and Tibshirani, R. J. (1993). An Introduction to the Bootstrap, Chapman Hall: New York.
- More literature ...
Cite correctly
Please always cite the use of SmartPLS!
Ringle, Christian M., Wende, Sven, & Becker, Jan-Michael. (2024). SmartPLS 4. Bönningstedt: SmartPLS. Retrieved from https://www.smartpls.com
