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Bootstrapping is typically used because the indirect effect is itself often nonnormal, which invalidated analytically-derived SEs and thus p-values and their corresponding 95% CIs. Bootstrap CIs have become the standard solution. However, Monte Carlo CIs can work reasonably well and the 95% intervals from a Bayesian analysis done with MCMC are also fine for nonnormal effects.

Hi Witold, you already got valuable advice by David an Solomon.

Here are my two cents:

"1. Why is it that some paths are significant without and become non-significant with bootstrapping is added? (Estimates [coefficients] do not change, but p values do)?"

-> If p-values change, this can only be due to different estimated standard errors (SE). Bootstrapping takes non-normality of the data into account, while SEs resulting from maximum likelihood estimation are based on the normality assumption.

"2. In example 1, total indirect effect and partial indirect effects are significant, despite the fact that the direct effect is still significant. Is that not weird? In that case, should not the direct effect be non-significant (A-D)?"

-> No, not necessarily. If the direct effect is still present after the mediator variable was added to the model, then the mediating variable accounts only for some, but not all of the relationship between predictor and criterion variable. This is called partial mediation as opposed to complete mediation, when the predictor variable no longer affects the criterion after the mediator variable has been controlled. Partial mediation is the case in which the path from predictor to criterion is reduced in absolute size but is still different from zero when the mediator is introduced.

"In conclusion, what method is superior? Should I just always use bootstrap if the sample is representative?"

-> If your sample size is large enough, bootstrapping should generally be superior.

Kind regards, Karin

Hi Karin,

Referring to your answer of first question, Can u explain more? I mean, is it a problem that some direct paths are significant without and become non-significant with bootstrapping is added? How can I explain it?

Hi Mahiuddin, David Boyda and Solomon Kurz already provided some answers concerning bootstrapping. Bootstrapping is often used for estimating standard errors of the direct and indirect effects. On the other hand, maximum likelihood (ML)also provides standard errors. Both estimations may be different depending in the distribution of the variables and sample size. Therefore, the method for estimating standard errors should be justified.

Therefore, if a direct path coefficient is significant using ML and this coefficient is non-significant using bootstrapping, then you should investigate the assumptions necessary for using each of the methods.

Kind regards, Karin

Thanks, Karin.