Ex9.10 r'slope factor
Message/Author
 Tino Nsenene posted on Friday, September 02, 2016 - 6:33 am
Hello,

why is y5 at the between-level in ex9.10 predicted by fb:

%BETWEEN%
fb BY y1-y4;
y1-y4@0;
y5 s ON fb w;

Would it be incorrect to model y5 as indicator of fb such that the syntax would read:

%BETWEEN%
fb BY y1-y5;
y1-y4@0;
s ON fb w;

Tino
 Bengt O. Muthen posted on Friday, September 02, 2016 - 10:11 am
Essentially, y5 is another factor indicator - that just happens to have a random slope. You would have to add y5 ON w to your second model for it to be the same as ex9.10.
 Tino Nsenene posted on Friday, September 02, 2016 - 10:45 am

And why should we regress the slope s on fb?

Intuitively, for me it is easy to grasp that the random slope of a facor indicator varies between groups, and that a certain group characteristic w account for part of this random variation.

But why should we regress s on fb, given that fb typically is used to model random variation in the intercepts of the indicators measured at the within-level?

Tino
 Bengt O. Muthen posted on Saturday, September 03, 2016 - 9:26 am
Regressing s on fb is done to see if larger factor values are associated with larger/smaller loading values.

To read about random slopes, see e.g. the papers on our website:

Asparouhov, T. & Muthén, B. (2015). General random effect latent variable modeling: Random subjects, items, contexts, and parameters. In Harring, J. R., & Stapleton, L. M., & Beretvas, S. N. (Eds.), Advances in multilevel modeling for educational research: Addressing practical issues found in real-world applications. Charlotte, NC: Information Age Publishing, Inc. Mplus scripts.

Muthén, B. & Asparouhov, T. (2016). Recent methods for the study of measurement invariance with many groups: Alignment and random effects. Download Mplus scripts.
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