Bootstrapping

• A resampling technique that draws a large number of subsamples from the original data (with replacement) and estimates models for each subsample.

• To determine standard errors of coefficient estimates to assess the coefficient's statistical significance without relying on distributional assumptions.

• The test will give indication whether the relationship is significant ie; statistically different from zero.

Why Bootstrapping?

1. Sampling distribution of indirect effect (a x b) is rarely to be normal (Hayes, 2013; Zhao et al., 2010).

2. It avoids statistical power problem of non-normal data of an indirect effect (MacKinnon et al., 2004).

3. It is applicable in small & moderate sample size with more confidence (Preacher & Hayes, 2008)

4. The results of bootstrapping is more trustworthy and powerful than other methods (Preacher & Heyes, 2008)

Example:

Is there a correlation between IQ & a methodology re-examination result?

Bootstrapping in Mediation/Indirect Effect

Indirect effect (path a x path b) should follow normal distribution (Hair et al., 2017). Based on Preacher and Hayes (2004; 2008), the suggested test for mediation/indirect effect is bootstrapping.

Ho: a*b = 0

H1: a*b ≠ 0

For each bootstrap sample, calculate a_i * b_i while creating the bootstrap t-statistics:

Bootstrapping, a nonparametric resampling procedure, has been recognized as one of the more rigorous and powerful methods for testing the mediating effect (Hayes, 2009; Shroud & Bolger, 2002; Zhao et al., 2010).

The application of bootstrapping for mediation analysis has recently been advocated by Hair et al. (2013) whom noted that “when testing mediating effects, researchers should rather follow Preacher and Hayes (2004, 2008) and bootstrap the sampling distribution of the indirect effect, which works for simple and multiple mediator models” (p. 223).

Furthermore, this method is said to be perfectly suited for PLSSEM because it makes no assumption about the shape of the variables’ distribution or the sampling distribution of the statistic and therefore can be applied to small sample sizes (Hair et al., 2013; Preacher & Hayes, 2008).