CONFIDENCE INTERVALS FOR MEDIATED PROPORTIONS

[eiovidal]

Dear SMART PLS masters,

Does anyone know how to extract confidence intervals for mediated proportions in SMART-PLS?
I know how to calculate the mediated proportions by dividing the total indirect effect by the total effect but calculating the confidence intervals for the mediated proportion is more complicated. Is there a way to extract that data from the output of SMAR-PLS analyses or to use the available output to calculate the confidence interval?

Kind regards,

Edison

[jmbecker]

In the Bootstrapping Output you can get the results for each bootstrapping subsample (check the box in the settings where it says "generate results per sample"). The you will get the results for all path coefficients, total effects, etc. under Algorithm > Samples > ...

You can copy these to Excel or any other Stats Software and calculate your metric of interest for each sample. For example the total indirect effect divided by the total effect. You can then easily calculate the percentile confidence intervals or standard deviations for this new estimate.

[eiovidal]

Dear jmbecker,

Thanks for your response. We had already done exactly what you advised us to do and were able to calculate the mediated proportion by dividing the total indirect effect by the total effect. However, we were not able to calculate the confidence interval for the mediated proportion. Indeed, when we divided the value of the 2.5 percentile of the total indirect effect by the 2.5 percentile of the total effect, the number that we found was incompatible with any reasonable expectations. We found this article about how to calculate those confidence intervals (see: https://cdn-links.lww.com/permalink/ede ... -00013.pdf) but were not able to implement that method using the data available in the output of SMART-PLS. Are you aware of any approach to extract the confidence interval for the mediated proportion directly from SMART-PLS or of using the already existing output to calculate that confidence interval?

Kind regards,

Edison

[jmbecker]

You cannot simply divide the confidence interval bounds. You need to do the division for each subsample. If you have used, for example, 10000 bootstrap samples, you need to copy all these 10000 samples (for example to Excel) and then divide the total indirect effect by the total effect. For these 10,000 new results you can calculate the 2.5% lower and upper bound using for example the quantile function in Excel. This would be bootstrap percentile intervals.

[eiovidal]

Dear Dr. Becker,

Finally, I understood what you meant! Many thanks! The idea is to generate the 10,000 bootstrap samples for total indirect effects and total effects followed by dividing those values for each sample so as to calculate 10,000 estimates for the mediated proportion. With those samples at hand, it is easy do calculate the confidence intervals using the quantile function from Excel. At this moment, the only thing that is hindering us from accomplishing this at this moment is that when we copy those results to excel the values that are copied are the numbers rounded to 2 decimal places, which in many cases ends up being zero. As a result, we had an entire column full of zeros. Are you aware of any means to be able to export those values to excel whilst keeping more decimal places?


Kind regards,

Edison

[jmbecker]

In the main menu of SmartPLS you find the "Preferences" and there you can set how many decimals you want to display in the reports.

[eiovidal]

Dear Dr. Becker,

We have followed your advice and were able to generate 1000 bootstrap samples for the total effect and the total indirect effect. We then created a new column for the mediated proportion and populated it with the results obtained by dividing the total indirect effect by the total direct effect. We then moved on to calculate both the mean value and the confidence interval for the mediated proportion on excel by using the means and percentile functions. To our surprise, the value for the mediated proportion and its confidence interval were 5.55 (0.32 to 4.48). Both the mean and the upper limit of the confidence interval are well above the 0 to 1 boundaries expected for proportions. We examined the numbers of the calculated mediated proportions and there were at least 300 samples where the mediated proportion was above 1, which does not make sense for a variable that should represent a proportion. Do you have any ideas about how to fix this so that we can arrive at the confidence interval for the mediated proportion?

Thank you,

Edison

[jmbecker]

The metric is only useful if you have a complementary mediation. Only if the total effect is always larger than the indirect effect, it will give a proportion. This is only the case if the direct effect equals indirect effect in sign (for all bootstrap samples).

Example:

Code: Select all

direct		indirect	total		indirect / total
-0.2		-0.3		-0.5		0.6
0.2		0.3		0.5		0.6
-0.2		0.3		0.1		3
0.2		-0.3		-0.1		3

That is also the reason why SmartPLS does not provide this metric. It is too rarely applicable and too often misleading and confusing.

[eiovidal]

Thank you so much for the clarification. in light of this new information, we gave up the idea of reporting the confidence interval for the mediated proportion,