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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; Many thanks for your response, Tino |
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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. |
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Tino Nsenene posted on Friday, September 02, 2016 - 10:45 am
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Thank you for your answer - I like the idea of modelling factor loading as random slopes - where can I read more about it? 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? Many thanks for your reply - Tino |
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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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