confidence interval for specific indirect effect

[Student84]

Dear experts,

I am writing my masters thesis and am using pls sem to calculate my results.
One thing that puzzels me and for which I have no been able to find an answer, is why the range of the confidence intervals for the specific indirect effects (studentized) which are calculated by hand with excel are so much smaller than the confidence intervals for other indirect effects calculated by pls sem.
The first would for example be only .002 while the latter can be as much as .200 while the means are similar.
I am following the directions of the book by Hair et al. (2016) and the template provided at the website of pls-sem.net
The template too shows a very small range for the confidence intervals of the specific indirect effects (studentized).
I suppose that as indirect effects are calculated as a product function of two direct effects, you would expect the resulting indirect effects to have smaller deviations, which would explain the outcome for the specific indirect effects, but then why is the range of the confidence intervals of the indirect effects (non-specific, non-studentized) calculated by pls sem so much bigger?

[jmbecker]

It would be good if you could show a specific example with numbers. Preferably from one of the example data sets that come with SmartPLS3. Then it is easier to understand your issue.

Two ideas:
1) Make sure that you also use studentized confidence intervals in SmartPLS.
2) The spread of the confidence interval depends on the standard deviation from boostrapping the parameter. If the STDEV from the specific indirect effect is smaller then the total indirect effect the confidence interval is also smaller.

[Student84]

Indirect Effects

Here's an example of an indirect effect calculated with pls sem. Note the large range of the confidence interval. 5000 bootstrap samples were used.

Mean, STDEV, T-Values, P-Values

Original Sample (O) Sample Mean (M) Standard Deviation (STDEV) T Statistics (|O/STDEV|) P Values
Y -> Z. 0,174 0,184 0,057 3,079 0,002


Confidence Intervals

Original Sample (O) Sample Mean (M) 2.5% 97.5%
Y -> Z. 0,174 0,184 0,084 0,307

Now below is an example of a specific indirect effect manually calculated with a much smaller range of the confidence interval. The variables are different of course because I am unable to calculate the specific indirect effect with pls sem for a multiple mediation model.

Confidence Intervals (Studentized)

Original Sample (O) Sample Mean (M) 2.5% 97.5%
V-->W via U. -0,106 -0,110 -0,107 -0,104

Confidence Intervals Bias Corrected (Studentized)

Original Sample (O) Sample Mean (M) Bias. 2.5% 97.5%

V-->W via U -0,106 -0,110 -0,004 -0,111 -0,109

Here is one from the example data set showing similarly small ranges for the confidence interval

Specific Indirect Effects


Mean, STDEV, T-Values, P-Values


Original Sample (O) Sample Mean (M) Standard Error (STERR) T Statistics (|O/STERR|) P Values
ATTR -> CUSA via COMP 0,000 -0,000 0,009 0,043 0,965
ATTR -> CUSA via LIKE 0,051 0,047 0,022 2,260 0,024
CSOR -> CUSA via COMP 0,000 -0,001 0,007 0,034 0,973
CSOR -> CUSA via LIKE 0,049 0,047 0,020 2,393 0,017
PERF -> CUSA via COMP 0,001 -0,000 0,027 0,047 0,962
PERF -> CUSA via LIKE 0,037 0,039 0,024 1,513 0,131
QUAL -> CUSA via COMP 0,002 -0,001 0,032 0,049 0,961
QUAL -> CUSA via LIKE 0,120 0,118 0,035 3,477 0,001


Confidence Intervals (Studentized)

Original Sample (O) Sample Mean (M) 2.5% 97.5%
ATTR -> CUSA via COMP 0,000 -0,000 -0,000 0,001
ATTR -> CUSA via LIKE 0,051 0,047 0,049 0,053
CSOR -> CUSA via COMP 0,000 -0,001 -0,000 0,001
CSOR -> CUSA via LIKE 0,049 0,047 0,047 0,051
PERF -> CUSA via COMP 0,001 -0,000 -0,001 0,004
PERF -> CUSA via LIKE 0,037 0,039 0,034 0,039
QUAL -> CUSA via COMP 0,002 -0,001 -0,001 0,004
QUAL -> CUSA via LIKE 0,120 0,118 0,117 0,123


Confidence Intervals Bias Corrected (Studentized)

Original Sample (O) Sample Mean (M) Bias 2.5% 97.5%
ATTR -> CUSA via COMP 0,000 -0,000 -0,001 -0,001 0,000
ATTR -> CUSA via LIKE 0,051 0,047 -0,004 0,045 0,049
CSOR -> CUSA via COMP 0,000 -0,001 -0,001 -0,001 -0,000
CSOR -> CUSA via LIKE 0,049 0,047 -0,002 0,045 0,049
PERF -> CUSA via COMP 0,001 -0,000 -0,002 -0,003 0,002
PERF -> CUSA via LIKE 0,037 0,039 0,002 0,037 0,041
QUAL -> CUSA via COMP 0,002 -0,001 -0,002 -0,003 0,002
QUAL -> CUSA via LIKE 0,120 0,118 -0,002 0,115 0,121

[jmbecker]

I have had a look at the Excel file from PLS-SEM.com and it is unfortunately not correct.

1) It uses the built-in Excel function confidence.t, which should not be used in a bootstrapping context. It gives intervals that are too narrow, because they use the number of bootstrap subsamples as degrees of freedom in the function, which shrinks the interval with increased number of subsamples.
Instead, you should calculate the interval as ORIG.COEF +/- T.INV(0.975;SUBSAMPLES)*SE.COEF. You can get the ORIG.COEF and the SE.COEF from the SmartPLS bootstrapping output.

2) Rather than using the studentized intervals, I would use the percentile intervals. They are also quite easy to calculate. Just use the QUANTILE function in Excel on the sorted SAMPLES output.

I have talked to Christian Ringle and I would guess an updated version of the Excel file will be uploaded soon.

[Student84]

Dear Mr. Becker,

Thank you for your reply and explanation.

I have used the second approach you suggested and have now calculated the specific indirect effect C.I's based on the percentile approach described by Nitzl et al., (2016), where "the lower bound is equal to the k × (.5 - ci% / 2)th ordinal position" and "the (1+k × (.5 + ci% / 2))th ordinal determines the upper bound".
The outcome is much more like what I would expect, a substanitally broader range.

Thanks again!