Question regarding higher-order factor model

[dhenderson17]

I have read over the posts in these forums and noticed that SmartPLS handles second-order factors. In my research model, I have seven first-order factors. Each first-order factor is reflective, composed of several items. Each of these first-order factors then becomes a formative indicator of two second-order factor (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 is whether SmartPLS can test this type of model? As I stated in the first sentence, I know SmartPLS handles second-order factors, but wasn’t sure if SmartPLS can handle a third-order factor.

[jjsailors]

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.

Conceptually the "third order" factor might be needed (and in covariance modeling perhaps computationally needed as well--if such a model could be identified) but in PLS I'm not sure that it's necessary, from the standpoint of the calculations.

Wouldn't the results be the same (computationally) is you simply use the second order constructs along with the two other factors to predict your dependent variable?

[dhenderson17]

Hello Dr. Sailors,

The two-second order constructs are formative, not reflective....would that make a difference? I'm not sure how that would affect the model....

Just read your answer again..do you mean to disgard the third-order factor and just have the two-second order factors? From a theoretical perspective, i don't think i should disregard the third-order factor....

Thanks for any help you can provide.

Best,

Dave

[jjsailors]

As I said, conceptually (theoretically) I understand that the 3rd order factor might be necessary.

I have have been wrong about the computational necessity, my mind thinking about it in covariance modeling terms.

How to do it? Treat the 3rd order factor the same as you would a second order factor, which means that you either 1) repeat all of the indicators of the 2nd order factors as its indicators or 2) create new indicators for it that are the LV scores from the second order constructs.

It gets cumbersome as you keep adding levels, but apart from that I don't think it matters whether you're talking about a 2nd order factor or an nth order factor, you specify it the same way.

[viswadatta]

Thanks a lot. I suppose you can do third order constructs as well using the same procedure.

But how do you test validity-convergent and discriminant for the constructs?

What are the quality factors apart from reliability. If some MVs are removed from the lower order constructs, then they should be removed from the higher order constructs as well, shouldn't they.

Regards

Vivek

[dhenderson17]

Hi Dr. Sailors,

Thank you again for your response. You mentioned two ways for computing the 2nd and 3rd order factors. Which way is the better way, or does the answer depend?

Also, I guess I wanted to double-check that Smart PLS can accomodate third-order factors. I know PLS-GRAPH can, but like i said, just wanted to double-check that Smart PLS can as well.

Thank you for all of your help.

Best,

Dave

[jjsailors]

Hi David,

First note that I've edited my response above, changing the 2nd option for how to set up second (or higher) order constructs.

In practice there should be little if any difference between the approaches. I've always simply repeated the indicators.

John

[dhenderson17]

Hi John,

Thanks for your help. I'm not sure how to do this in Smart PLS yet, but I'm in the early stages of using the tool. As I continue to use Smart PLS, I should be able to figure out the exact mechanics of how to setup the second and third order factors.

As a side question, I conducted a power analysis last night for my study and determined that I need approx. 115 subjects to achieve a power of .8 (alpha=.05, medium effect size of .15). This analysis is based upon 9 independent variables. I do, however, have a covariate in my study, but I can't find any literature that discusses the impact of a covariate on sample size. I'm also not sure if Smart PLS can handle a covariate. I looked through the forum, but didn't see any posts that really answered this question.

Any advice would be much appreciated. Thanks again for your help.

Best,

Dave

[viswadatta]

I also have a doubt. In PLS no error terms are mentioned explicitly. What happens if two error variables are correlated? This will falsely show a significant path between two variables, even though only their errors are related.

[jjsailors]

I also have a doubt. In PLS no error terms are mentioned explicitly. What happens if two error variables are correlated? This will falsely show a significant path between two variables, even though only their errors are related.

I think that's not correct. It's not that error terms aren't explicitly stated, it's that they play no role in the model.

An Emergent Variable (EV) is always a weighted sum of it's manifest variables, and, while the estimation of those weights may imply an error term, that term plays no role in the calculation of the EV.

Likewise when calculating path coefficients between EVs, the error term from one equation is irrelevant to the other equations that may also involve the same EV because each is, again, just the weighted sum of it's manifest variables.

[am00019]

"What are the quality factors apart from reliability. If some MVs are removed from the lower order constructs, then they should be removed from the higher order constructs as well, shouldn't they. "

Hello,

I didn't see an answer to Viswadatta's question above. Do you remove items below .7 for second order and third order constructs when using repeated indicators?

Thanks,

Alex

[jmbecker]

On the higher-order construct where you repeat the indicators, loadings must not be above 0.7. It is not a normal measurement model, but only auxiliary measurement.

[am00019]

Thanks for the response. To be clear, on 2nd order construct reliability should be less than 0.7 ?

Seems counter intuitive since we always want reliability greater than 0.7 if possible.

We have good reliability on our first order constructs that repeat as indicators for the 2nd order.

When we run PLS, some reliabilities on the 2nd order construct are in .6 range.

Shouldn't these items be removed?

Thanks,

Alex

[jmbecker]

If you remove items from the first order constructs you remove them also from the second-order (and higher) constructs.
On the first order constructs all normal rules apply (e.g., loadings should be higher than 0.7) and if you need to delete due to these rules you also delete on the SO construct.
However, on the SO constructs loadings need not to be higher than 0.7. They can be higher, but also lower. This does not matter. Decisions for retaining indicators are only made on the first oder constructs and then tranfered to the higher order constructs.