New rules for keeping formative indicators

Frequently asked questions about PLS path modeling.
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AAljabr
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Real name and title: Abdulrahman Aljabr

New rules for keeping formative indicators

Post by AAljabr » Thu Feb 25, 2016 2:03 pm

Dear SmartPLS users and developers,

Hope you are doing well. Can you comment and give answers to the points below.

1. Hair et al. (2013) and Cenfetelli and Bassellier (2009) proposed a rule regarding keeping formative indicators, which states that formative indicators with insignificant weights can be kept if their loadings are high (i.e., above .5) and/or significant. In relation to this rule, I have one question, which I present after an example of a situation. Assume that a formative construct (PC) is influencing an endogenous construct (CSC). If one of the formative indicators of PC (let us say PC1) has insignificant weight, but has a high and/or significant loading on the construct PC. I decided to keep this formative indicator (i.e., PC1) based on the rule mentioned above (i.e., based on the loading not the weight), how should I interpret the influence of PC1 on the final endogenous construct CSC?

2. Becker et al. (2013) proposed a rule regarding the preferable usage of Mode A instead of Mode B for formative constructs (under some conditions). Becker et al. (2013) pointed out how Mode A weights (i.e., correlation weights) are slightly different from the Mode A loadings, and that Mode A weights (i.e., correlation weights) should be interpreted in a similar way to Mode B weights (i.e., regression weights).

1.I did not understand the exact difference between Mode A weights and loadings. Can anyone elaborate more about this?

2.Assuming a formative construct (PC) is influencing an endogenous construct (CSC), and assuming using Mode A for the formative construct (PC), how should I interpret the influence of the formative indicators of PC on the final endogenous construct (CSC)?

3.Is it possible to use Hair at al. (2013) and Cenfetelli and Bassellier (2009) rule while using Becker et al. (2013) rule of using Mode A for formative constructs? i.e., Is possible to use Mode A for formative constructs, and keep formative indicators that have insignificant weights but high and/or significant loading?

Thanks

Becker, J.-M., A. Rai, C. M. Ringle and F. Völckner (2013). "Discovering unobserved heterogeneity in structural equation models to avert validity threats." Mis Quarterly 37(3): 665-694.

Cenfetelli, R. T. and G. Bassellier (2009). "Interpretation of formative measurement in information systems research." Mis Quarterly: 689-707.

Hair Jr, J. F., G. T. M. Hult, C. Ringle and M. Sarstedt (2013). A primer on partial least squares structural equation modeling (PLS-SEM), Sage Publications.

AAljabr
PLS Expert User
Posts: 33
Joined: Wed Jan 06, 2016 11:52 pm
Real name and title: Abdulrahman Aljabr

Re: New rules for keeping formative indicators

Post by AAljabr » Sun Mar 06, 2016 10:52 am

Dear SmartPLS developers and Experts,

We all would benefit from your advice about this issue.

Thanks

jmbecker
SmartPLS Developer
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Real name and title: Dr. Jan-Michael Becker

Re: New rules for keeping formative indicators

Post by jmbecker » Tue Mar 15, 2016 7:53 pm

1. The problem of insignificant weights yet high loadings is multicollinearity. Two (or more) indicators might be highly correlated. This implies that they probably both contribute to the constructs and, hence, deletion would not be good as you would delete one important dimension of the formative construct. Especially, as multicollinearity makes estimates unstable (dancing around). On the population-level, multicollinearity is not a big problem and the correct weight might show a higher influence, but on the sample-level, it could be that with different samples different indicators have a significant/insignificant weight. You might delete the wrong indicator based on the idiosyncrasies of your sample.

2. Both Mode A and Mode B are just ways to estimate the weights of the composite. Regardless of the composite being reflective or formative. You can use Mode A with a formative construct as you may use Mode B with a reflective constructs.
The latter may not be wise, because reflective indicators should exhibit high multicollinearity and Mode B estimation accuracy suffers from multicollinearity. In contrast, Mode A does not have such a problem. That is way Mode A might be useful for formative indicators as well, if they exhibit collinearity between the indicators.
And how do we then separate reflective from formative constructs?
For reflective constructs, the estimated loadings are important and you want to assess them.
For formative constructs, the estimated weights are important and you want to assess them.

You can apply the same rules on weights estimated with Mode A or Mode B for you formative construct. It is just a different way to estimate the weights. It does not change the way you assess your formative construct.
Dr. Jan-Michael Becker, University of Cologne, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Jan_Michael_Becker
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de

AAljabr
PLS Expert User
Posts: 33
Joined: Wed Jan 06, 2016 11:52 pm
Real name and title: Abdulrahman Aljabr

Re: New rules for keeping formative indicators

Post by AAljabr » Wed Mar 16, 2016 6:57 pm

Dear Dr. Becker,

Many thanks for your valuable answers and responses. Let me clarify my question.

1. There are many examples in the literature who assessed the influence of each of the formative indicators on the final endogenous construct by multiplying the formative item weight (e.g., PC1 weight) by the beta coefficient of the influence of the formative construct (e.g., PC) on the final endogenous construct (e.g., CSC). However, these examples evaluated and kept the formative items based on their weights using, I suppose, Mode B.
If, however, a researcher follows (1) Hair et al (2013) and Cenfetelli and Bassellier (2009) rule, and therefore kept some items that have insignificant weight but high or/and significant loading, or (2) Becker et al (2013) rule of using Mode A instead of Mode B, how the researcher should evaluate the influence of PC1 on the final endogenous construct (CSC) and not the formative construct itself?

2. You are right and I understand your point that researcher should assess Mode A weights in case of formative constructs, but please clarify what is the exact difference between Mode A weights and Mode A loading? it is still not clear to me.

Many thanks,
Abdulrahman

MrcJnk
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Re: New rules for keeping formative indicators

Post by MrcJnk » Thu Mar 17, 2016 1:18 pm

Dear Mr. Aljabr:

1. Assuming that you do not have any multicollinearity problem as described by Dr. Becker, I use the following common example of drunkenness to provide a possible interpretation for insignificant regression weights. You could measure drunkenness formative as the extent to which you have drunken glasses/shots of beer, wine and whiskey. You aim to investigate the cause of drunkenness on the fitness for driving. In your sample there are just a few individuals which drive under alcohol when they have drunken whiskey. The path coefficient between drunkenness and the fitness for driving could be significantly negative while the regression weight of the number of whiskey shots could be insignificant in this model. Nevertheless, the number of drunken whiskey shots could be meaningful for your construct drunkenness! You should not drop this item.

2. Maybe you should try to change the mode for your measurement model in Smartpls and then look at the outcome to better understand what influence the change of the measurement mode has. To calculate the latent variable score of a specific construct there is just mode A or mode B available. The direction of the arrows from the items (construct) to the construct (items) determines if your construct is of formative (reflective) nature. On the basis of the direction of your arrows you will finally obtain regression (formative) or correlation (reflective) weights as outcome to interpret your results. If you do not set the mode manual, then Smartpls automatically uses mode A for the calulation of your latent variable score when your arrows point in the direction of the items (reflective) and finally you will get correlation weights as outcome for your interpretations. When your arrows point in the direction of the construct (formative), Smartpls automatically uses mode B for the calculation of your latent variable score and you will get regression weights as outcome for your interpretations. I guess thats the difference: Irrespectively which direction your arrows have, the mode determines how your latent variable scores are calculated and finally how your path coefficients are estimated. The direction of your arrows determines if you interpret your results by regression weights or correlation weights (loadings).

Thats my level of knowledge after reading the literature and after some estimations with changed modes and arrow directions in Smartpls. Please correct me, if I am wrong!

Best regards

MJ

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