Question on repeated indicator approach

[dhenderson17]

Hello all,

I have read over the posts in these forums and noticed that SmartPLS handles second-order factors using the repeated indicators approach. In my research model, I have seven first-order factors. Each first-order factor is reflective, composed of several indicators. Each of these first-order factors then becomes a formative indicator of two second-order factors (3 first-order factors go to the first second-order factor and 4 first-order factors go to the other second-order factor). These two second-order latent factors then serve as formative indicators for a third-order factor. The third-order factor, along with two other factors, is used to predict the dependent variable.

My question relates to the actual mechanics of implementing the repeated indicators approach in SmartPLS. From my understanding of how the repeated indicators approach is handled in SmartPLS, I would:

1) Assign the indicators to their respective first order factors. I would NOT invert the measurement model, as the first order factors are reflective.

2) Reassign the indicators for the first order reflective factors to their respective second order formative factors. Since the second order factors are formative, I would the invert the measurement model (make them formative) for the second order factors.

3) Reassign all the indicators for the reflective first order factors, which were assigned to their respective second order formative factors (see step 2 above), to the third order factor. Since the third order factor is formative, I would invert the measurement model (make it formative) for the third order factor as well.

In this scenario, it would appear that each indicator is assigned 3 times: once to its respective first order factor, once to its respective second order factor and once to the third order factor.

Does this sound correct? Any help would be much appreciated.

[viswadatta]

Yes you are right. Use the same quality parameters to judge reliability and validity of factors.

[dhenderson17]

Thank you for your response! Your help is much appreciated.

So, just to clarify your response:

1) I am using the repeated indicators approach correctly.
2) I should use composite reliability, AVE to judge reliability and construct validity of the higher order factors

Thanks again for your help!

[Salima]

Hi David,

very interesting and helpful summary of handling second order constructs.

Do you have any literature concerning the step 2 (inverting the measurement model by reassigning the former reflective indicators to the second order construct)?
The alternative would be to reassign the reflective indicators in a reflective way to the formative second order construct (see Wold 1982).

Thanks,
Salima

[viswadatta]

Reliability is measure using cronbach's alpha for any type or order of construct, ave is used for measuring convergent validity under construct validity. You can also measure discriminant validity among the subconstructs of each second order construct using ave and construct correlations. These are the quality parameters for any order of constructs.

[yuanho]

Thank you for the above questions and answer.

When I applied the above strategy of my research model (first-order construct is reflective, second-order construct is formative) in smartPLS, there will be the AVE value on the report. But if I viewed both first-order and second-order construct as formative, the AVE is null on my smartPLS report. Please tell me why? Thank you very much.

[viswadatta]

That is od, it should run, see if you have assigned all indictors properly and re do the algorithm

[yuanho]

Thank you for the reply.

When I manipulate my formative construct, the only thing I did is to press the construct and then use ALT+Y (Invert measurement model), I did not change any indicators. Is the procedure right?

When I remain all the constructs as reflective construct, then there will be the AVE, but once I change any reflective construct as the fromative construct (I only applied the above step to reverse the directions of arrow), then the AVE of the formative construct is "0".

[viswadatta]

Try using factor scores as indicators for second order constructs and do only a first order model, that way you will avoid confusion

[bwilson]

Dear all,

Unless i am reading this incorrectly, do not report these statistics for the formative section of your analysis.