How to calculate the number of Tetrad?

[ouxiancai]

Hi to all!
I have conducted a Confirmatory Tetrad Analysis for a construct with five reflective indicators(A1-A5) using SmartPLS 3.0, then it produced a result output just for 5 tetrads as below (also seen in the attachment):
1: A1,A2,A3,A4
2: A1,A2,A4,A3
4: A1,A2,A3,A5
6: A1,A3,A5,A2
10: A1,A3,A4,A5
I just wonder:
(1) what does the number ( 1 2 4 6 10 )mean;
(2) how to calculate the number of independent tetrads;
(3) why the tetrad of (A1,A2,A4,A5) and (A2,A3,A4,A5) were not showed in the result output?

Many thanks for your help！

[cringle]

Please take a look at these articles, which provide you with the detailed answers to your questions:

Bollen, K. A., & Ting, K.-f. (1993). Confirmatory Tetrad Analysis. In P. V. Marsden (Ed.), Sociological Methodology (pp. 147-175). Washington: American Sociological Association.

Bollen, K. A., & Ting, K.-f. (2000). A Tetrad Test for Causal Indicators. Psychological Methods, 5(1), 3-22.

Gudergan, S. P., Ringle, C. M., Wende, S., & Will, A. (2008). Confirmatory Tetrad Analysis in PLS Path Modeling. Journal of Business Research, 61(12), 1238-1249.

Best
CR