Mapping LVs to another LV without Indicator Variables

[writz]

I have a model where I need 2 or 3 latent variables (each with their own indicator variables) to go into another latent variable that does NOT have any indicator variables. I spent some time playing with SmartPLS trying to figure this out but I haven't found a solution. Does anyone know how to do this? Or even if what I am trying to do is possible?

Thank you,
Westley Ritz

[jjsailors]

I have a model where I need 2 or 3 latent variables (each with their own indicator variables) to go into another latent variable that does NOT have any indicator variables. I spent some time playing with SmartPLS trying to figure this out but I haven't found a solution. Does anyone know how to do this? Or even if what I am trying to do is possible?

Thank you,
Westley Ritz

PLS can't accommodate this sort of model.

[writz]

I was handed the model and asked to relipcate it in PLS; after playing with it in SmartPLS, I was having my doubts as to whether this model was appropriate. I appreciate your feedback.

Thank you,
Westley Ritz

[ghozali]

What do you meant by latent variable without indicator? Is it observed variable? If it is observed variabel, you just put the observed indicator (one indicator) to the latent variable as formative indicator (arrow toward VL) instead of reflexive indicator

Imam Ghozali

[writz]

No, it is not an observed variable. I was attempting to map two latent variables (call them A and B with their respective observed indicator variables a1, a2, b1, b2) to a third latent variable (call it C). C does not have any indicator variables and is not observed. Thus, I was trying to have A and B map to C as if A and B were the indicator variables for C. Then perhaps I would map C to another LV later along the path, but my problem lies in mapping A and B to C. I hope that makes more sense.

Thank you,
Westley Ritz

[jjsailors]

I was handed the model and asked to relipcate it in PLS

It's either
a) a test
b) the person who asked you to run it doesn't understand PLS or
c) if it was claimed to be estimated originally via PLS then the person/organization that originally ran it lied.

But, the model that you describe sounds like the intent might be for C to be a second order factor. In PLS the way you would do this is by repeating the measures for A and B and using them as indicators for C.

So A1 and A2 cause A, B1 and B2 cause B and A1,A2,B1 and B2 cause C.

[writz]

Well, the model was supposedly originally done with PLS, but that's all the information that I have. After looking at it with another collegue, we had our doubts and figured we only had half of the truth as to how the model was constructed. But we decided to see if it was possible to replicate it using PLS anyway. With your help, John, I came to the conclusion that this is not possible. The idea of a second order model is interesting, but I'm not sure of the interpretation of it. I've been reading through posts in the forum, but I need to do some more research on this topic. Is there a good article you can suggest that may clear this up for me?

Thank you,
Westley Ritz

[jjsailors]

The idea of a second order model is interesting, but I'm not sure of the interpretation of it. I've been reading through posts in the forum, but I need to do some more research on this topic. Is there a good article you can suggest that may clear this up for me?

Thank you,
Westley Ritz

Unfortunately, no. Not specific to the PLS context. The idea of second order factors is used just as it is in covariance based modeling, but to my knowledge the testing of the meaning of the repeated measures approach in PLS has not been rigorously tested.

[viswadatta]

Second order models can be calculated by repeating indicators to the second order construct.

Otherwise try out visualPLS at
http://fs.mis.kuas.edu.tw/~fred/vpls/

The software still does not provie a bootstrap for second order models

[Michaela Dietz]

Hallo,

sorry that I don´t understand your suggestion. But what do you mean by "repeating indicators to the second order construct?"
Because we also want to form the second order latent variables formative by the first order latent variables without using an indicator for the second oder variable.

[viswadatta]

Consider two first order constructs C1 and C2. Assume C1 has indicators I1 and I2, while C2 has I3 and I4. Assume C3 as a second order construct that has subconstructs C1 and C2.

In the above situation draw C1 and C2 first with appropriate indicators. Now draw C3 and assign all four indicators(I1 to I4) a second time to C3. Now raw arrows from C3 to C1 and C2. Your diagram is ready.

Note that each indicator appears twice in each diagram!

I hope this helps.

[dhenderson17]

wouldn't you draw the arrows from the first order constructs (C1 & C2) to the second order construct (C3) rather than drawing the arrows from the second order construct (C3) to the first order constructs (C1 & C2)?

[viswadatta]

Either way is OK depending on the nature of your construct(fomative/reflective)

[Michaela Dietz]

Thank you for your explanation. But I´ve got still a question:
Assume C3 should not be measured by indicators at all, because we want to assume that C1 and C2 have to be understood like indicators for C3 (formative). We would insert a new LV called C4. An arrow would connect C3 und C4 (from C3 to C4) and we would just measure C4 by indicators, e.g. like you explained. Is that possible????