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 Michael J. Zyphur posted on Thursday, April 13, 2006 - 1:42 am
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!

cheers,
mike

Skrondal, A. and Laake, P. (2001). Regression among factor scores. Psychometrika 66, 563-575.
 Bengt O. Muthen posted on Thursday, April 13, 2006 - 4:57 pm
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.
 Michael J. Zyphur posted on Thursday, April 13, 2006 - 9:24 pm
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)?

Thanks for your time,
mike
 Bengt O. Muthen posted on Friday, April 14, 2006 - 1:04 am
Not sure.
 Michael J. Zyphur posted on Friday, April 14, 2006 - 8:17 am
Hmm, let me try to desribe a different way: Is the expected a posteriori distribution of slopes a distribution of scores which solve for Y given a known value of X and a fixed intercept?

Again, thanks for your time!
mike
 Bengt O. Muthen posted on Friday, April 14, 2006 - 11:39 am
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.
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