[100 Multilevel Questions]Modeling Changes in HLM?

Dear Tom,

Thank you very much for your explanation. I see your point, but in addition to the concerns raised by Malcolm I also wonder one more thing: Wouldn’t this same argument also be an argument against estimating a random intercept at the person level (for the dependent variable) in a longitudinal design? Because estimating a random intercept leaves for level 1 the within-person deviations from the mean, i.e. more or less the same thing as you would get when mean-centering?

Just to add my 2 cents - my view of mean centering (and using mean variables generally) is that when measuring the mean you are trying to measure the effect of latent variables for which the mean acts as a proxy, rather than the effect of the mean per se.  So, to take the original example, the mean stress of an individual is really a proxy for the many individual characteristics (personality traits, etc) that are related to stress.  In measuring this proxy variable you want as much information as possible, and therefore using future information is no bad thing since that information is relevant to the time invariant characteristics of the individual.

So for me, it is less saying the future influences the past (which it probably doesn't), than that the future is relevant to the individual's time-invariant characteristics (which it probably is).  Therefore, if you are interested in deviations from an individuals 'norm', you would get potentially 'better' estimates by mean centering than centering on t=1 (given that t=1 may have been exceptional and not representative of an individuals t-invariant characteristics).

Hope that is helpful - would also be interested to know peoples thoughts on this.

Best wishes
Andrew Bell

No, because my argument applies only to observed variables. The random intercept is a latent variable.

Best regards,

Tom Snijders

Dear Tom,

Interesting, in that case perhaps the best option is to use Muthén’s Latent Covariate Model, in which a random intercept is estimated for the independent variable?

Lüdtke, O., Marsh, H. W., Robitzsch, A., Trautwein, U., Asparouhov, T., & Muthén, B. (2008). The multilevel latent covariate model: A new, more reliable approach to group-level effects in contextual studies. Psychological Methods, 13(3), 203–229. doi:10.1037/a0012869, 10.1037/a0012869.supp (Supplemental)

Muthén, B., & Asparouhov, T. (2011). Beyond multilevel regression modeling: Multilevel analysis in a general latent variable framework. In J. J. Hox & J. K. Roberts (Eds.), Handbook for advanced multilevel analysis. (pp. 15–40). New York, NY US: Routledge/Taylor & Francis Group. Retrieved from http://search.ebscohost.com/logi ... amp;site=ehost-live