Mixed higher order constructs

 PLS Expert User
 Posts: 33
 Joined: Wed Jan 06, 2016 11:52 pm
 Real name and title: Abdulrahman Aljabr
Mixed higher order constructs
Dear all,
I have two second order constructs. Some of the first order constructs are reflective and others are formative. The relationship between all of the first order constructs and the second order construct is formative.
Now if I want to use the repeatedindicator approach, which mode (A or B) should I use for:
1. The formative first order constructs.
2. The formative second order construct (note: this construct consists of both reflective and formative first order constructs).
Related literature suggests the following:
1. In case of having reflectiveformative constructs (i.e., reflective first order constructs which have a formative relationship with the second order construct), Becker et al. (2012) suggested using Mode B for the second order construct which, again, has a formative relationship with the first order constructs.
2. In case of formative constructs, Becker et al. (2013) recommended Mode A when the sample size is not too small. However, I do not know whether this recommendation is also applicable to second order formative constructs.
The question is which mode is better to be used when having the following types of higher order constructs and the repeated indicator approach is to be used instead of the two stage approach:
1. FormativeFormative: formative first order constructs, formative second order constructs.
2. Mixed: both formative and reflective first order constructs, formative second order constructs.
Based on Becker et al. 2013, I assume that using Mode A is recommended for all formative constructs (either first order or second order) when using the two stage approach.
Thanks
Becker, J. M., Klein, K., & Wetzels, M. (2012). Hierarchical latent variable models in PLSSEM guidelines for using reflectiveformative type models
Becker, J. M., Rai, A., & Rigdon, E. (2013). Predictive validity and formative measurement in structural equation modeling Embracing practical relevance.
I have two second order constructs. Some of the first order constructs are reflective and others are formative. The relationship between all of the first order constructs and the second order construct is formative.
Now if I want to use the repeatedindicator approach, which mode (A or B) should I use for:
1. The formative first order constructs.
2. The formative second order construct (note: this construct consists of both reflective and formative first order constructs).
Related literature suggests the following:
1. In case of having reflectiveformative constructs (i.e., reflective first order constructs which have a formative relationship with the second order construct), Becker et al. (2012) suggested using Mode B for the second order construct which, again, has a formative relationship with the first order constructs.
2. In case of formative constructs, Becker et al. (2013) recommended Mode A when the sample size is not too small. However, I do not know whether this recommendation is also applicable to second order formative constructs.
The question is which mode is better to be used when having the following types of higher order constructs and the repeated indicator approach is to be used instead of the two stage approach:
1. FormativeFormative: formative first order constructs, formative second order constructs.
2. Mixed: both formative and reflective first order constructs, formative second order constructs.
Based on Becker et al. 2013, I assume that using Mode A is recommended for all formative constructs (either first order or second order) when using the two stage approach.
Thanks
Becker, J. M., Klein, K., & Wetzels, M. (2012). Hierarchical latent variable models in PLSSEM guidelines for using reflectiveformative type models
Becker, J. M., Rai, A., & Rigdon, E. (2013). Predictive validity and formative measurement in structural equation modeling Embracing practical relevance.

 PLS Expert User
 Posts: 33
 Joined: Wed Jan 06, 2016 11:52 pm
 Real name and title: Abdulrahman Aljabr
Re: Mixed higher order constructs
Dear all,
Your answers and opinions are highly appreciated.
Thanks
Your answers and opinions are highly appreciated.
Thanks

 PLS Expert User
 Posts: 33
 Joined: Wed Jan 06, 2016 11:52 pm
 Real name and title: Abdulrahman Aljabr
Re: Mixed higher order constructs
Dear SmartPLS developers and Experts,
We all would benefit from your advice about this issue.
Thanks
We all would benefit from your advice about this issue.
Thanks

 PLS User
 Posts: 16
 Joined: Thu Oct 17, 2013 10:04 am
 Real name and title: Marc Janka
 Location: Germany
Re: Mixed higher order constructs
Dear AAljabr
I have already asked myself this question a few days ago. The following is my understanding from reading the literature and trying out some stuff. Mode A and Mode B lead to quite similar results when sample size is high (Becker et al., 2013, p. 16). I have tried it with different sample sizes and there seems to be merely small differences when sample sizes are n > 200. Further, the initiator, Lohmöller (1989), himself did not provide any suggestions in which way higher order constructs should be modeled (Becker et al., 2012, p. 366). Therefore, I would only use Mode B for the higher order construct if the indicators of the lower order construct are formative and sample size is even small. In all other cases I would use Mode A for the higher order construct when applying the repeated indicator approach. For mixed cases it is quite tough to say because I guess there cannot be a final "true" answer. Perhaps this would be the only case were I would think about using the hybrid approach, i.e., hold back one indicator for each lower order construct and then use all of the retained indicators with Mode B for the higher order construct.
This is just the way I would do it after reading the literature and trying some things out.
Best regards
MJ
*Edit: Of course, applying the hybrid approach in the way I have described it above would be best when there is one indicator available that represents the whole formative lower order construct, e.g., having a formative measured construct for customer satisfaction that is measured by the two formative indicators "friendliness of employees" and "expertise of employees" and one indicator that represents the "overall customer satisfaction". A huge extent of the variance of the "overall customer satisfaction" item should be explained by the two formative indicators as it is shown in Götz et al. (2011) or described in Hair et al. (2014).
Götz, O., LiehrGobbers, K., & Krafft, M. (2011). Evaluation of Structural Equation Models Using
the Partial Least Squares (PLS) Approach
Hair, J. F., Hult, G. T. M., Ringle, C. M., & Sarstedt, M. (2014). A Primer on Partial Least Squares Structural Equation Modeling (PLSSEM)
I have already asked myself this question a few days ago. The following is my understanding from reading the literature and trying out some stuff. Mode A and Mode B lead to quite similar results when sample size is high (Becker et al., 2013, p. 16). I have tried it with different sample sizes and there seems to be merely small differences when sample sizes are n > 200. Further, the initiator, Lohmöller (1989), himself did not provide any suggestions in which way higher order constructs should be modeled (Becker et al., 2012, p. 366). Therefore, I would only use Mode B for the higher order construct if the indicators of the lower order construct are formative and sample size is even small. In all other cases I would use Mode A for the higher order construct when applying the repeated indicator approach. For mixed cases it is quite tough to say because I guess there cannot be a final "true" answer. Perhaps this would be the only case were I would think about using the hybrid approach, i.e., hold back one indicator for each lower order construct and then use all of the retained indicators with Mode B for the higher order construct.
This is just the way I would do it after reading the literature and trying some things out.
Best regards
MJ
*Edit: Of course, applying the hybrid approach in the way I have described it above would be best when there is one indicator available that represents the whole formative lower order construct, e.g., having a formative measured construct for customer satisfaction that is measured by the two formative indicators "friendliness of employees" and "expertise of employees" and one indicator that represents the "overall customer satisfaction". A huge extent of the variance of the "overall customer satisfaction" item should be explained by the two formative indicators as it is shown in Götz et al. (2011) or described in Hair et al. (2014).
Götz, O., LiehrGobbers, K., & Krafft, M. (2011). Evaluation of Structural Equation Models Using
the Partial Least Squares (PLS) Approach
Hair, J. F., Hult, G. T. M., Ringle, C. M., & Sarstedt, M. (2014). A Primer on Partial Least Squares Structural Equation Modeling (PLSSEM)

 PLS Expert User
 Posts: 33
 Joined: Wed Jan 06, 2016 11:52 pm
 Real name and title: Abdulrahman Aljabr
Re: Mixed higher order constructs
Dear MJ,
Many thanks for your response.
I agree with you that there is no definitive answer.
Based on my reading, I would advise using the twostage estimation approach for both situations (i.e., formativeformative, and mixed higher order constructs). For the first stage, I would use Mode A for formative and reflective first order constructs. In stage two, I would use also Mode A. Based on Becker et al. (2013), Mode A provides more stable weights in case of multicollineraity.
Best,
Abdulrahman
Many thanks for your response.
I agree with you that there is no definitive answer.
Based on my reading, I would advise using the twostage estimation approach for both situations (i.e., formativeformative, and mixed higher order constructs). For the first stage, I would use Mode A for formative and reflective first order constructs. In stage two, I would use also Mode A. Based on Becker et al. (2013), Mode A provides more stable weights in case of multicollineraity.
Best,
Abdulrahman
 cringle
 SmartPLS Developer
 Posts: 812
 Joined: Tue Sep 20, 2005 9:13 am
 Real name and title: Prof. Dr. Christian M. Ringle
 Location: Hamburg (Germany)
 Contact:
Re: Mixed higher order constructs
@1: Mode BNow if I want to use the repeatedindicator approach, which mode (A or B) should I use for:
1. The formative first order constructs.
2. The formative second order construct (note: this construct consists of both reflective and formative first order constructs).
@2: I never used mixed models and there is no standard solution; Mode A
Also take a look at (see the appendix):
Ringle, C. M., Sarstedt, M., and Straub, D. W. 2012. A Critical Look at the Use of PLSSEM in MIS Quarterly, MIS Quarterly, 36(1), iiixiv.
http://misq.org/skin/frontend/default/m ... sV36N1.pdf
Prof. Dr. Christian M. Ringle, Hamburg University of Technology (TUHH), SmartPLS
 Literature on PLSSEM: https://www.smartpls.com/documentation
 Google Scholar: https://scholar.google.de/citations?use ... AAAJ&hl=de
 Literature on PLSSEM: https://www.smartpls.com/documentation
 Google Scholar: https://scholar.google.de/citations?use ... AAAJ&hl=de

 PLS Expert User
 Posts: 33
 Joined: Wed Jan 06, 2016 11:52 pm
 Real name and title: Abdulrahman Aljabr
Re: Mixed higher order constructs
Dear Prof. Ringle,
Many thanks for your response.
Based on the above, and given that you pointed out the possibility of using Mode A for the second order formative construct, would it be also appropriate to use Mode A for the first order formative constructs in this situation?
I am saying this because I think I also need to be consistent. If I use Mode A for the second order formative construct, I need to use the same mode for the first order formative constructs.
In general, which method do you advocate? two stage approach or the repeated indicator approach?
Becker, J. M., Rai, A., & Rigdon, E. (2013). Predictive validity and formative measurement in structural equation modeling Embracing practical relevance.
Many thanks for your response.
I understand that Mode A might be suitable for my mixed higher construct that have a formative relationship with all of the first order constructs (note: some of the first order are reflective and others are formative). When using the repeated indicator approach, the second order construct will have arrows pointing from/to (1) the first order constructs, and (2) the indicators of these first order construct. In relation to (1), the arrows will be directed from the first order constructs to the second order construct because they are formative indicators to the second order construct. However, in relation to (2), how should I model the arrows from the first order constructs' indicators to the second order construct. This is because some of these indicators have a reflective relationship with their first order construct, while others have a formative relationship with their first order construct.2. The formative second order construct (note: this construct consists of both reflective and formative first order constructs).
@2: I never used mixed models and there is no standard solution; Mode A
I forgot to say that I have a problem of negative and insignificant weights. According to Becker et al. (2013), using Mode A for formative constructs is recommended in these situations (note: there are some conditions related to sample size and rsquare).1. The formative first order constructs.
@1: Mode B
Based on the above, and given that you pointed out the possibility of using Mode A for the second order formative construct, would it be also appropriate to use Mode A for the first order formative constructs in this situation?
I am saying this because I think I also need to be consistent. If I use Mode A for the second order formative construct, I need to use the same mode for the first order formative constructs.
In general, which method do you advocate? two stage approach or the repeated indicator approach?
Becker, J. M., Rai, A., & Rigdon, E. (2013). Predictive validity and formative measurement in structural equation modeling Embracing practical relevance.

 PLS Junior User
 Posts: 3
 Joined: Thu Jun 20, 2019 12:13 pm
 Real name and title: PhD Estibaliz Rodriguez Nuñez
Re: Mixed higher order constructs
"some of these indicators have a reflective relationship with their first order construct, while others have a formative relationship with their first order construct"... I have the same case now, how did you solve the situation? Thanks in advance.