How to test "nesting effects" in a linear model after you have reduced the IV by factor analysis? I have a couple items (let's say 10) had run in a study and I want 1) to reduce the dimensions by factor analysis.
Then I have two factors (let's say factor A has 3 and factor B has 7 items). After that, I want to run a linear model with these compound factors. The factors will be the IV.
Now my actual questions: I want to control for nesting effects, because in factor B, 7 datapoints are always from the same participants.
Do you know how to do this? I use LM in R. (Is this even a SEM thing?)
Thank you for any idea!
 A: My advice, follow this work Factor Analysis Scores in a Multiple Regression Model for the Prediction of Carcass Weight in Akkeci Kids (free). To quote from the Abstract:

In this study, the relationships between carcass weight and 10 body measurements (slaughter weight, withers height, body length, chest depth, chest width, chest circumference, leg circumference, leg width, leg length and rump width) were examined through factor and multiple linear regression analyses. It was observed that three factors e.g. Form, Circumference and Wideness had significant effects on carcass weight and these factors together accounted for 83.9% of variation in carcass weight.

Now, to address, "Now my actual questions: I want to control for nesting effects, because in factor B, 7 datapoints are always from the same participants." The author states:

Factor scores can be derived such that they are nearly uncorrelated or orthogonal. Thus the use of factor scores as the variables in other analyses is possible and may be very helpful (Tabachnick and Fidell, 2001).

So, nesting issues was mitigated as the author further stresses:

In order to facilitate interpretation of factor loadings (Lik), VARIMAX rotation was used.

I would advise, to confirm a valid model specification, that you can (or upon consultation with knowledge sources) be able to ascribe for the constructed explanatory 'forms' (per the terminology above) some fundamental understanding as to why they are (and should continue to be) true underlying driving forces.
