How to see the bootstrap mediation effect

The Bootstrap method to evaluate the mediating effect includes: 1. Perform regression analysis to record the direct effect and indirect effect; 2. Split sampling and repeatedly calculate the mediating effect to construct a confidence interval; 3. Compare the confidence interval to determine whether the indirect effect is Significant, and assess how well it explains the total effect.

Bootstrap mediation effect evaluation method

The Bootstrap method is a statistical inference method that can be used to evaluate the mediation effect. The mediating effect means that an independent variable indirectly affects the dependent variable by affecting the mediating variable.

Steps:

1. Perform regression analysis

• Use bootstrapping to analyze the independent variable X and the mediating variable M Perform regression analysis on the relationship between the dependent variable Y.
• Record the direct effect (c') and indirect effect (a*b) of X on Y.

2. Split sampling

• Randomly select multiple subsamples (for example, 1000 subsamples) from the original sample.
• For each subsample, repeat the following steps:

3. Calculate the mediation effect

• Calculate the mediation for each subsample Effect, that is: indirect effect = a*b
• Calculate the confidence interval of the direct effect, indirect effect and total effect.

4. Compare confidence intervals

• Compare the confidence intervals of direct effects and indirect effects. A mediating effect is considered to exist if the confidence interval for the indirect effect does not include zero.
• Compare the confidence intervals for indirect effects and total effects. If the confidence interval for the indirect effect is small relative to the confidence interval for the total effect, it indicates that the mediating effect partially explains the effect of X on Y.

Example:

Suppose we study the relationship between the independent variable (gender) and the dependent variable (salary), and consider the mediating variable (education level) .

• Regression analysis shows that the direct effect of gender on wages is 0.2, and the 95% confidence interval is [0.1, 0.3].
• The indirect effect is 0.1, and the 95% confidence interval is [0.05, 0.15].
• The total effect is 0.3, and the 95% confidence interval is [0.2, 0.4].

According to the confidence interval, the indirect effect is significant and not zero, indicating that education level plays a mediating role in the impact of gender on wages. Furthermore, the confidence interval for the indirect effect is about one-third of the confidence interval for the total effect, which means that education level partially explains the effect of gender on wages.

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