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Based on Preacher & Hayes (2008), a significance of indirect effect through a certain mediator is obtained by multiplying two unstandardized paths via that mediator in each of the bootstrap sample and then compute the Confidence Interval. In the case of BCa Bootstrap, each path has it's own Bias so each path will have different index of the lower and upper bound of the Confidence Interval. So how do you obtain bias corrected and accelerated bootstrap confidence interval for the indirect effect that consist of two path with different bias?
i'm using smartpls 3 and i only got the BCa CI for each corresponding path

Preacher, K.J. & Hayes, A.F. Behavior Research Methods (2008) 40: 879. doi:10.3758/BRM.40.3.879

Best Regards,

I Putu Ariyasa

According to Preacher & Hayes you calculte the indirect effect by multiplying the direct paths via the mediator and then bootstrap them. Hence, you get an own bias for the indirect effect (which is the product of the coefficients) and lower and upper bounds.

Thanks for the answer.

can this be done on smartpls3? or if it can't, is there any software that could compute the bias and determine the CI using the bootstrap samples generated by smartpls3?

Yes, SmartPLS 3 implements this approach.

I see, i've have been searching too in the meantime and found out that the "Indirect Effect" in the bootstrap report represent the significance of the total mediation effect. But what i didn't found is BCa CI mediation effect for each mediator in the case of multiple mediation. Can this also be done in the smartpls3?

Yes, but with the current version (3.2.6) only with some extra calculations. An example Excel sheet is provided on http://www.pls-sem.com
The next, version 3.2.7, which will be released soon, will include those specific indirect effects with all necessary calculations.

jmbecker wrote:Yes, but with the current version (3.2.6) only with some extra calculations. An example Excel sheet is provided on http://www.pls-sem.com
The next, version 3.2.7, which will be released soon, will include those specific indirect effects with all necessary calculations.

By an example Excel, did you mean excel file named "TESTING OF MULTIPLE MEDIATION USING A MODIFIED VERSION OF THE CORPORATE REPUTATION MODEL" provided at this link : https://www.pls-sem.net/app/download/15 ... 1485782413 ?

If so, then i have tried using the formula by replacing the original sample value, mean, std error, and bootstrap sample count (5000), but it gives different CI or Bias Corrected CI from the one produced by smartpls3.

I noticed that there is a "studentized" notation in the excel. Does this mean the confidence interval should be interpreted differently from the one produced by smartpls (that is if the CI contain 0, then the result is not significant) ?

Hereby i attached the screenshot

The interpretation of the intervals is the same regardless of method for calculating the interval bounds (i.e., studentized, percentile, bca, etc.).

However, please also read the following forum thread viewtopic.php?f=5&t=16109

jmbecker wrote:The interpretation of the intervals is the same regardless of method for calculating the interval bounds (i.e., studentized, percentile, bca, etc.).

However, please also read the following forum thread viewtopic.php?f=5&t=16109

I've seen the link and applied your correction to the excel file, but the result is still different. Isn't the computation of BCa much more complicated than just decreasing the percentile interval by it's bias. I've read "An Introduction to the Bootstrap" by Bradley Efron & R.J. Tibshirani and find it hard to translate the formula into excel spreadsheet.

The bias correction for the percentile approach is quite easy. Calculating the third order moments for the acceleration is more complicated.
To get the bias correction for the percentiles you have to:
1) Count the number of subsamples where the parameter is smaller than the original sample estimate (you can use “countif” if in Excel).
2) Then you need to calculate the lower and upper bounds using the following formula in Excel:
Lower = No.Subsamples*NORMSDIST(2*NORMSINV(COUNT/No.Subsamples)+NORM.S.INV(Alpha/2))
Upper = No.Subsamples*NORMSDIST(2*NORMSINV(COUNT/No.Subsamples)-NORM.S.INV(Alpha/2))
Lower and Upper gives you a number in the sorted list of parameter estimates from the subsamples. The value of the parameter from that subsample is your lower and upper confidence level.
You can see that this is the formula that you have attached. If the acceleration a is zero, the formula reduces to Phi(2*z0+za)

jmbecker wrote:Calculating the third order moments for the acceleration is more complicated.

Yes, how to do this in excel is what i have been searching for lately. i suppose that excel is not quite the right tool for this. i guess i need to wait the version 3.2.7 for the time being or report the Bias Corrected interval for the specific indirect effect.

Thanks for your guidance Sir.

Well, the questions is: do you necessarily need the BCa interval?
For example, Hayes process tool in SPSS, which is quite popular for standard (non PLS) multiple mediation models, also does not provide BCa intervals, but only simple bias-corrected percentile intervals. Those that you can also easily calculate by hand.

well, the reason i'm trying to use BCa for the specific mediation was simply because smartpls 3 report the BCa CI for the total mediation effect and other pls result.

Sure, but you can also get simple bias corrected percentile intervals using the percentile approach in SmartPLS.

oh, i didn't know that percentile intervals also showed the bias corrected interval. i'll try it then. Thank you very much