Abstract

Bootstrapping is a nonparametric procedure that allows testing the statistical significance of various PLS-SEM results such path coefficients, Cronbach’s alpha, HTMT, and R² values.

Brief Description

PLS-SEM does not assume that the data is normally distributed, which implies that parametric significance tests (e.g., as used in regression analyses) cannot be applied to test whether coefficients such as outer weights, outer loadings and path coefficients are significant. Instead, PLS-SEM relies on a nonparametric bootstrap procedure (Efron and Tibshirani, 1986; Davison and Hinkley, 1997) to test the significance of estimated path coefficients in PLS-SEM.

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 PLS path model. This process is repeated until a large number of random subsamples has been created, typically about 10,000.

The parameter estimates (e.g., outer weights, outer loadings and path coefficients) obtained from the subsamples are used to derive the 95% confidence intervals for significance testing (e.g., original PLS-SEM results are significant when they are outside the confidence interval). In addition, bootstrapping provides the standard errors for the estimates, which allow t-values to be calculated to assess the significance of each estimate.

Becker et al. (2023) and Hair et al. (2022) explain bootstrapping in in PLS-SEM 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):

1. Percentile Bootstrap (default)
2. Studentized Bootstrap
3. 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.

Random number generator

The algorithm randomly generates subsamples from the original data set, which requires a seed value for the random number generator. You have the option to choose between a random seed and a fixed seed.

The random seed produces different random numbers and therefore results every time the algorithm is executed (this was the default and only option in SmartPLS 3).

The fixed seed uses a pre-specified seed value that is the same for every execution of the algorithm. Thus, it produces the same results if the same number of subsamples are drawn. It thereby addresses concerns about the replicability of research findings.

References

• Becker, J.-M., Cheah, J. H., Gholamzade, R., Ringle, C. M., Sarstedt, M. (2023): PLS-SEM’s Most Wanted Guidance, International Journal of Contemporary Hospitality Management, 35(1), pp. 321-346.

• 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 ...