Hi Bengt or Linda, I was wondering if either of you could tell me how Mplus computes factor scores if I request them for a random slope -- both a random slope used at the same level on which it was created and at a higher level of analysis.
Would the factor scores for a same-level random slope be the person-specific b-weights? Additionally, for the multilevel random-slope model (a within-groups slope made random at the between-groups level), would the groups' factor scores be b-weights?
In any event, do you think that traditional arguments levied against using factor scores as DVs (e.g., Skrondal & Laake, 2001) would be applicable to factor scores of random slopes?
Thanks for your time, and I hope everything is going well in Los Angeles!
Skrondal, A. and Laake, P. (2001). Regression among factor scores. Psychometrika 66, 563-575.
In this context, factor scores are computed using the expected a posteriori method. I don't know what person-specific b-weights are. Yes, I think traditional arguments against factor scores hold here as well.
By person-specific b-weights I guess I just meant the derivative of the DV for each person given a fixed intercept. Would the expected value for each person/group along the random slope be such a derivative (i.e., the way to solve for Y given a fixed intercept and a known X value)?
I don't think that is how it should be viewed. The posterior distribution is the distribution of a slope given the observed data. The mean of that distribution is then taken as the point estimate for that cluster. A simpler example is regular factor analysis, where the posterior distribution for the factor given the observed vector is normal. Here the expectation is the same as the mode (the max). This is the same as the "regression method" of factor score estimation.