About composite variables-based models

[Julian Gaviria]

Dear List,

My ultimate research aim is to identify whether one or multiple aspects (i.e. indicators)  of  "CURRENT BODY STATE"  mediate the interaction between  one or multiple  indicators of "PREVIOUS BODY STATE"  and one or multiple  indicators of "PERFORMANCE" .

Hypothesis: Only some indicators from  "CURRENT BODY STATE" but not all of them  play a key role in the  interaction between "some" indicators (but not all) from PREVIOUS BODY STATE"  and "some" indicators (but not all) from "PERFORMANCE". 

Two aspects are important to keep in mind: First, despite the fact that indicators represent clustered data (i.e. correlation between the indicators of each variable), it is critical to determine (i.e., quantify) their individual roles. Second, the  nature of the indicators captures the full universe of the variables. Namely, the variables are entirely made up of the indicators. For this reason, I think I need to model my data with composite variables instead of latent ones.

Question1:  Would you agree with my rationale? Or, is it rather more appropriate/efficient to model a latent variable-based model?

Assuming that composite variables modelling is the right way to go,  two preliminary steps would implement two different multilevel models to  identify those indicators with significant values in the regressions.

Step A. Multilevel regression inspecting the interaction between the indicators of "CURRENT BODY STATE"   and the indicators of "PERFORMANCE".  

Step B. Multilevel regression inspecting the interaction between the indicators of "PREVIOUS BODY STATE"   and the indicators of "PERFORMANCE". 

To note, I did not check the interaction: "PREVIOUS BODY STATE" - "CURRENT BODY STATE" because my study is focused on "PERFORMANCE". Thus, any indicator with no significant interaction with another indicator from "PERFORMANCE", would be beyond the scope of this study.   

Question 2:   Is this way the most efficient one?  Or would you rather suggest  any other option to identify the "main" indicators (i.e., those with significant associations)?  

Subsequently in step C,  I would compute a composite variables-based model  including only those indicators with significant values.

Question 3:  Again, if composite variables are the right direction, I wonder how I could get a "clear" example of computing such composite variables with lavaan. It is my understanding that this package does not do this automatically.

Many thanks in advance, 

Julian Gaviria 

Neurology and Imaging of cognition lab (Labnic)

University of Geneva. Campus Biotech. 
9 Chemin des Mines, 1202 Geneva, CH

Tel: +41 22 379 0380 

Email: Julian.Ga...@unige.ch