Confirmatory Tetrad Analysis to assess constructs

[spiking]

1. How to use the SmartPLS to determine whether a construct should be formative or reflective?

=> Please show the detailed steps in SmartPLS.

2. Results from SmartPLS are different from what is shown in:
Gudergan, S.P., Wende, S. & Will, A., 2008. Confirmatory tetrad analysis in PLS path modeling. Journal of Business Research, 61(12), pp.1238–1249.

=> Please see attachments and advise how to extract data for the respective columns from SmartPLS.

Thank you!

[spiking]

Please help.

Anyone please give advice?

[jmbecker]

Gudergan et al. (2008) describe five steps:

1. Form and compute all vanishing tetrads for the measurement model of a latent variable.
2. Identify model-implied vanishing tetrads.
3. Eliminate redundant model-implied vanishing tetrads.
4. Perform a statistical significance test for each vanishing tetrad.
5. Evaluate the results for all model-implied non-redundant vanishing tetrads per measurement model by accounting for multiple testing issues.

When you use the CTA procedure in SmartPLS 3, you don’t have to worry about steps 1-3. This will be done automatically and you will get the result for step 4. Thus, you only have to do step 5, i.e., the evaluation of the results.

Important for your assessment is the significance of each tetrad.

You get results for each construct that has at least 4 indicators (this is the minimum requirement, but the paper also describes a procedure how to borrow indicators from other constructs if you have only three indicators).

If you click on the constructs you find the results that show the significance test for the non-redundant tetrads from a bootstrapping procedure. In a reflective measurement model the tetrads should be nonsignificant, so your p-values should be higher than 0.05.
A different approach to assess significance is the evaluation of confidence intervals which should include zero (i.e., are not significant) for reflective measures. Because you actually test multiple tetrads at the same time, we also perform a Bonferroni adjustment for the multiple tests at the same time for the confidence intervals.

A measurement model is formative if it includes at least one significant tetrad.

It seems that you have a lot of significant tetrads (p values < 0.05), hence, you have a formative measure.

[spiking]

Dear Dr. Becker

Thank you so much for your enlightenment!!!

It certainly makes so much sense now!

[spiking]

In Table 4.10 below, it shows the significance tests for the non-redundant vanishing tetrads from a bootstrapping procedure. In a reflective measurement model, the vanishing tetrads should be non-significant, and the resulting p Values should be higher than 0.05. However, as shown in the last column, the p Values were lower than 0.05. Therefore, this implies that the vanishing tetrads were significant, and the measurement model comprising of Actual Social Action was formative.

[Wenjing Li]

“the paper also describes a procedure how to borrow indicators from other constructs if you have only three indicators”. Could you please give more details about how to do this, by what procedure and how to realize this is the SmartPLS 3.0?
Thanks.

Dear Dr. Becker

Thank you so much for your enlightenment!!!

It certainly makes so much sense now!

[jmbecker]

The procedure is discribed in the paper. It can be easily adapted in SmartPLS 3.

[Wenjing Li]

The procedure is discribed in the paper. It can be easily adapted in SmartPLS 3.

As to the latent variable with less than four manifest variables, “carrying out the CTA-PLS procedure requires adding manifest variables from measurement models of other latent variables and reducing the number of model-implied vanishing tetrads”. There still exists some doubtful points, waiting the guidance from you.
My doubts are as follows:
(1) the paper (CTA-PLS; Gudergan et al., 2008) says that “The analytical purposes of this study require a modification of the original correlation matrix. Absolute correlation values of manifest variables in the outer models below 0.1 become subject to a systematical increase in their absolute value by 0.1 (e.g., 0.08 to 0.18 or −0.01 to −0.11). This modification is important because neither CTA-SEM nor CTA-PLS are applicable for correlations or covariances close to zero in the measurement model (Bollen and Ting, 2000). ” I just doubt that whether this modification is included in the CTA analysis in SmartPLS3 or I should do this firstly and then go the the CTA Algorithm in SmartPLS3.

(2) “Each latent variable E1 and E2 has three indicators in a reflective measurement model. In both cases, CTA-PLS analyses the mode of the measurement model by using one manifest variable from the measurement model of the other latent variable.” While to the “using one manifest variable from the measurement model of the other latent variable”, I just wonder the selection of the manifest variable from the measurement model of the other latent variable is randomly or should according to some rules. For example, there may be several latent variable and several manifest variables in each latent variable measurement model. So, how I select the “borrowed manifest variable”, just randomly, or, according to the correlation of manifest variables and selected the moderate correlated (or high related) ones.

(3) To realize the CTA in SmartPLS3. My solution is below (see Figure 1--original and Figure 2--the revised for CTA Algorithm), just adding a manifest variable (cusa) from the near latent variable (CUSA-cusa) and the similar handling to other latent variables with no more that three manifest variables. The calculation results are in Table 1. Is the cognitive above is right, or there are some wrong issues exist? Could you help me?

Figure 1 Original Model

Figure 2--the revised model for CTA Algorithm

Table 1 the results of CTA Algorithm




Thanks for your attention.
Waiting for your reply.

[cringle]

Thanks for your email and your good questions:

@(1): No, this is not included in SmartPLS. The researcher must conduct this analysis (it's a kind of data manipulation that we do not automatize). For example, when running SmartPLS 3, you get the correlation matrix of indicators as one of the results. -> PLS Algorithm -> Results Report -> Basic Data -> Indicator Data (Correlations).

@2: Yes, you are right about this issue. The recommendations of Bollen and Ting are also a bit vague. I believe that we wrote in the JBR article that you chose the dependent variable with the highest correlation and the indicator with the highest loading in that measurement model. If there is no dependent latent variable, you choose the predecessor with the highest correlation and its indicator with the highest loading. In both ways, it should be the indicator of a successor or predecessor with the highest correlation with the latent variable scores of the construct that need an additional indicator. For that purpose, you could also take a look at the cross loadings in the discriminant validity results table.

In the example you may want to use this



or that approach



If I am not mistaken, LIKE and CUSA support the reflective orientation, while COMP rejects it in both cases when choosing a 2-sided test and a 10% probability of error and 5000 bootstraps.

For COMP, you must decide from a content point of view if it is formative or reflective.

@3: Just answered.

All the best to your research and kind regards
Christian

[Wenjing Li]

[Dear Dr. Christian,
Thanks for your interpretation, with my heartful thanks.

Warm regards,
Jing

[asukur]

Hello,

My question is related to CTA for hierarchical component model (HCM), also known as the repeated indicators. Should I run CTA in SMARTPLS3 on an original or the HMS after creating LOC and HOC. Also, any resources that you would recommend that could help me to interpret results from CTA in SMARTPLS3.'

Thank You!

Anita

[asukur]

Hello,

My question is related to CTA for hierarchical component model (HCM), also known as the repeated indicators. Should I run CTA in SMARTPLS3 on an original or the HMS after creating LOC and HOC. Also, any resources that you would recommend that could help me to interpret results from CTA in SMARTPLS3.'

Thank You!

Anita

[skono]

Greetings from Canada,

I am running some confirmatory tetrad analyses (CTA), following Gudergan et al.'s (2008) procedures with SmartPLS 3. In so doing, I've got a few basic questions and am wondering if somebody could help me out! My questions are:

(a) Gudergan et al. (2008) reported "residual values" in Tables 4 and 5 (pp. 1244 and 1246, respectively). I am not sure where in SmartPLS 3 outputs we can find these values. Given that some of values they reported have a negative sign, I suspect that these are not standard deviation or error... Perhaps, values under the "Original Sample (o)" in the output?

(b) In the first post from Spiking, Spiking's CTA output includes "standard error." But, my output shows "standard deviation." I am wondering if I did something wrong...

Any comments would be greatly appreciated!

All the best,

Shin

[mnabi]

Hi everyone,

I have a construct that can be formative or reflective (it has three formative and two reflective indicators). I collected data for all of these indicators.I want to identify the mode of this construct to be used in my measurement model. Can I use confirmatory tetrad analyses (CTA) for all of the indicators and decide according to the result of analysis? As you maybe know, CTA needs at least four indicators. Or, Is it just better to use a "borrowed manifest variable"?

All problems are for the reason that we can not measure MIMIC models in SmartPLS. Am I right? Is there any other way for that? For example, I found sth like this: "If the reflective items are measuring exactly the same facet of the construct, and the content validity of the construct would not be affected, all of the reflective items except one could be removed from the measure. The result would be a construct that has the same content validity (if the correlated items are interchangeable) as the original construct, and the researcher would be left with a purely formative construct". But I don't know it is practical or not.

Best,

[mnabi]

Hello,

In the table of CTA-PLS, we have confidence interval and adjusted confidence interval (CI low and up adj.). Which one should I use for analysis? Is it something about Bonferroni-corrected and bias-adjusted confidence interval?

Thanks.