# Path Analysis and PROCESS Bootstrapping

## Abstract

Bootstrapping is a nonparametric procedure that can be used to test the statistical significance of various path analysis and PROCESS results such as path coefficients.

## Brief Description

SmartPLS uses bootstrapping to determine the significance of estimated path analysis and PROCESS coeffiecients. 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 preocedure 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., 1000) 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.

## 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. BÃ¶nningstedt: SmartPLS. Retrieved from https://www.smartpls.com