Path Analysis and PROCESS Bootstrapping
Bootstrapping is a nonparametric procedure used to test the statistical significance of path analysis and PROCESS results, such as path coefficients, without requiring assumptions about the underlying population distribution. SmartPLS uses bootstrapping to determine the significance of estimated path analysis and PROCESS coefficients by repeatedly re-estimating the model on resampled data.
How Bootstrapping Works
In bootstrapping, subsamples are created with randomly drawn observations from the original set of data (with replacement). The subsample is then used to estimate the path analysis and PROCESS model. This procedure is repeated until a large number of random subsamples has been created, typically about 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 with observations drawn at random from the original dataset (with replacement). The number of observations per bootstrap subsample is identical to the number of observations in the original sample (SmartPLS also considers 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 assessment, one may wish to choose a smaller number of bootstrap subsamples (e.g., 1,000) to be randomly drawn and estimated with the PLS-SEM algorithm, since that requires less time. For the final results preparation, however, one should use a large number of bootstrap subsamples (e.g., 10,000).
Note: Larger numbers of bootstrap subsamples increase the computation time.
Do Parallel Processing
If chosen, the bootstrapping algorithm will be performed on multiple processors (if your computer offers more than one core). As each subsample can be calculated individually, subsamples can be computed in parallel mode. Using parallel computing will reduce computation time.
Confidence Interval Method
Sets the bootstrapping method used for estimating nonparametric confidence intervals. The following bootstrapping procedures 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 percentile bootstrapping. If you have concerns about a non-normal bootstrap distribution, you can alternatively use bias-corrected and accelerated (BCa) bootstrapping.
Test Type
Specifies if a one-sided or two-sided significance test is conducted.
Significance Level
Specifies the significance level of the test statistic.
Frequently Asked Questions
Why is bootstrapping needed for path analysis and PROCESS results?
Bootstrapping is a nonparametric procedure, so it lets you test the statistical significance of path coefficients and other results without assuming a specific population distribution. It works by repeatedly estimating the model on randomly resampled subsamples and using the resulting parameter estimates to derive confidence intervals and standard errors.
How many bootstrap subsamples should I use?
For an initial assessment, a smaller number of subsamples (e.g., 1,000) is sufficient and faster to compute. For final results, use a larger number of subsamples (e.g., 10,000) to ensure the stability of the results, keeping in mind that more subsamples increase computation time.
Which confidence interval method should I choose?
Percentile bootstrapping is the default and generally recommended method. If you are concerned about a non-normal bootstrap distribution, bias-corrected and accelerated (BCa) bootstrapping is a suitable alternative. Studentized bootstrapping is also available.
What is the difference between a one-sided and two-sided significance test?
The test type setting specifies whether SmartPLS evaluates significance using a one-sided or a two-sided test, which affects how the significance level is applied to the test statistic.
Does enabling parallel processing change the bootstrapping results?
No. Parallel processing only distributes the computation of subsamples across multiple processor cores to reduce computation time; it does not change how the subsamples are drawn or how the results are calculated.
Related SmartPLS Methods
References
- Hair, J. F., Hult, G. T. M., Ringle, C. M., & Sarstedt, M. (2027). A primer on partial least squares structural equation modeling (PLS-SEM) (4th ed.). Sage.
- Davison, A. C., & Hinkley, D. V. (1997). Bootstrap methods and their application. Cambridge University Press.
- Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. Chapman & Hall.
- 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
