Hello,
i have a big question about second order factor. When it's reflexive there is no problems. But when it's formative ???
See on the picture below:
What is the good situation ??
-In the first the end of arrows of hidden indicators are from Variable 4 to indicators
-In the second, inverse : from hidden indicators to the V4
-In the third there is not need to add hidden indicators.
Where error and why ?
I'm a bit lost could you help me please.
I have read some literature of Chin in this way but not precisely on the formative variable case.
Your measurement of the second order construct is a typ II modulation. That means, in the first order you use reflektiven measurements and in the second order you use a formative measurement. For estimate such a model you should use the suggested method by Wold which is depicted in figure 2. Here some literature for that:
Lohmöller, J.-B. (1989): Latent Path Modeling with Partial Least Squares, Heidelberg, p. 130.
Wold, H. (1982): Soft Modeling: The Basic Design and Some Extensions, in: Jöreskog, K./Wold, H. (Hrsg.): Systems Under Direct Observations: Causality, Structure, Prediction, Part 2, Amsterdam, S. 40.
As in situation 2 above, would calculating VIF means regressing each of the indicators from indic1 to indic6 in spss or is there any other way to do this?
In the above mention situation 2 you have reflective items in the first and second order measurement. Therefore it is not necessary to calculate VIF. It is only necessary when you use formative measurements. But you are right in the current program version of PLS you have to use e.g. SPSS for calculate VIF.
Hi,
Actually I would advise you to model situation 1. If you use situation 2 you will probably get very similar weights (path coefficients) for V1-V3 on V4 unless you have no multicollinearity at all.
If you use situation 1 you will get weights (path coefficients) for V1-V3 on V4 that can exhibit different magnitudes and represent the formative nature of that hierarchical component more closely.
Why? If you use situation 2 than every indicator (1-6) will contribute to V4 almost equally (at least in most situations), because of nearly equal loadings and therefore weights of the mode A estimation.
An exception is the case where you have no correlation between Indc1-Indc6. In this case, situation 1 and 2 should be equal.
If you use situation 1, the mode B estimation of the hierarchical component will give different weights to the different indicators and therefore also different weights for the path between the lower-order components V1-V3 and the higher-order component V4.
However, as Lohmöller notes, you will have problems with identification in this situation. That’s why he does not advise this type of estimation (mode B on the hierarchical component). That problem, however, only occurs if you do not have a subsequent endogenous construct in your model to which the higher-order component is linked, i.e. if you want to estimate the hierarchical component separately.
As you have such a construct V5, identification should be no problem and you gain the advantage of interpreting the relative effect of each lower-order component on the higher-order component as in a formative measurement model.
Hello,
Thank's a lot Dr Becker. I've tried the two modes (inverting the hidden indicators) but there is really few differences between the two meaures and the ratio between the links of two indicators seems to be conserved. I'll try to see it more in details.
I have another question relative to second order : my second order factors have an R squared = 1 or 0.99 is there a problem ?
Hi,
Actually no, that is not a problem and should be this ways, because your higher-order component is completely explained by its lower-order components.
However, this becomes a problem if you have antecedent constructs to your hierarchical component, e.g. any V6 that predicts V4. In such a situation you will always get an insignificant path of close to zero, because the hierarchical component is already fully explained.
In such a situation you should first evaluate if the antecedent is not actually also a component of the hierarchical construct and if it is conceptually distinct you should model a path from V6 to V1 to V3 and assess the total effect from V6 on V4, instead.
Hi Dr Becker,
thank's again.
could you tell me the reference of the book of Lohmöller you use and moreover the number of interesting interval of pages . I'll ask university's library, to demand it at international (lending between libraries in Europa) because i can't find the book of Lohmöller 1989 nowhere ! (i ask for pages beacause for numerous books, foreign libraries don't send the book just a copy of needed pages...
Thank you very much for this interesting conversation. I found it very helpful.
Regarding noone's question, I am facing the same problem with my second order construct (dependent). I obtain R2 = .99 and the path coeficient = Zero.
I found this article (Ringle et al. 2012/MISQ) interesting and addresses this problem.
(Ringle et al 2012) A Critical Look at the Use of PLS-SEM in MIS Quarterly
The authors note (in p.8):
"In half of the formative–formative type and in a quarter of the reflective–formative type of hierarchical component model applications, the
higher order component is endogenous. These model set-ups require particular attention when the repeated indicators approach is used since
almost all variance of the higher order component is explained by its lower order components (R² . 1.0; Figure B2). As a consequence, the
path relationship from the latent variable (predecessor) to the endogenous higher order component is always approximately zero and
nonsignificant".
Then, the authors introduce the solution:
"In this kind of situation, a mixture of the repeated indicators approach and the use of latent variable scores in a two-stage approach—which
is similar to the two-stage approach in moderator analyses in PLS-SEM (Henseler and Chin 2010)—is appropriate. In the first stage, one uses
the repeated indicators approach to obtain the latent variable scores for the lower order components which then, in the second stage, serve as
manifest variables in the measurement model of the higher order component (Figure B2). Thereby, the higher order component is embedded in the nomological net in a way that allows other latent variables as predecessors to explain some of its variance, which may result in significant path relationships".
I hope this help.
I am not sure how to go through these steps. I will return to (Henseler and Chin 2010). However, I would be thankful if anyone can help by more tips/ how to apply.
