Some details about confirmatory tetrad analysis

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Joined: Wed Aug 17, 2016 4:02 pm
Real name and title: Shintaro Kono, Ph.D Candidate

Some details about confirmatory tetrad analysis

Post by skono » Thu Jun 08, 2017 7:49 pm

Hi all,

I am finalizing my manuscript, where I mostly used confirmatory tetrad analysis (CTA) following Gudergan et al.'s (2008) procedures. I found one (detail) issue in one of their findings, and am wondering if anyone can jump in and address it (perhaps, I am misreading or so):

In Table 5 (p. 1246), Gudergan et al. (2008) reports that the "percentage of absolute correlation values below 0.1" for Loyalty is 17%. But, they also says "The only exception is the evaluation of the latent variable Loyalty. Correlations of 0.05, 0.10, and 0.54 among the three manifest variables are at least in one case too close to zero to reasonably apply CTA-PLS" (p. 1245). So, there are 3 correlations among the 3 indicators, one of which is below .10. Shouldn't this be reported as .33% as the percentage of absolute correlation values below 0.1? An only possible explanation I can think of is that they included three diagonal correlations (r =1 for each of the indicators) into the calculation, which does not seem informative to me.

Plus, I also realized that SmartPLS 3 (v3.2.4) does not show the percentage of absolute correlation values below 0.1 in CTA outputs. It would be nice if this feature is included in the future versions.

All the best,


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Real name and title: Prof. Dr. Christian M. Ringle
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Re: Some details about confirmatory tetrad analysis

Post by cringle » Sat Jun 10, 2017 9:12 am

Thanks for your kind feedback and suggestions. The correlations just require a quick inspection to ensure that the tetrad does not vanish because of the differences but because there is no correlation in the product of correlations. For example, tetrad_1234 = corr_12 * corr_34 - corr_13 * corr_42 and you expect the tetrad to vanish. If the correlations are almost zero, the will be "automatically" the case. Then you would not reject the null hypothesis that you consider a reflective measurement model. But having no correlation of the indicators makes it difficult to establish a reasonable reflective measurement model. Hence, we provide the rule of thumb for the a priori inspection of correlations.


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