R: st: baseline adjustment in linear mixed models

[Formoso Giulio <GFormoso@regione.emilia-romagna.it>]

Updating my previous post of about 2 hours ago (see below): analyzing data as Clyde proposed (vs introducing baseline values as covariate, as I did before), confidence intervals widen if, as unit of analysis, I use health districts (n=42), whereas become much narrower if I use physicians (N=about 4000).
Giulio

-----Messaggio originale-----
Da: Formoso Giulio 
Inviato: lunedì 11 febbraio 2013 11:46
A: statalist@hsphsun2.harvard.edu
Oggetto: R: st: baseline adjustment in linear mixed models

Thank you Clyde for your kindness and clarity. If I compare intervention and control areas, their baseline values look much closer than their post-intervention values (curves clearly divaricate when the intervention starts). I don't know if, under these circumstances, baseline (pre-intervention) values  could be considered as distinctively influential as you say (if you have time, I'd like your opinion on this point). Actually I tried your alternative analysis: intervention vs control difference does not substantially change, although confidence intervals are wider.  

Thank you again! Giulio

-----Messaggio originale-----
Da: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di Clyde B Schechter
Inviato: domenica 10 febbraio 2013 00:03
A: statalist@hsphsun2.harvard.edu
Oggetto: Re: st: baseline adjustment in linear mixed models

Giulio Formoso raises a question that comes up from time to time on Statalist: he plans to do a linear mixed model analysis of repeated-observations on a sample of units of observation, and asks if it is appropriate to include the baseline outcome value as a covariate.

Back to basics.  Let's think about a very simple statistical model that could be analyzed with the command:

-xtmixed y || participant: -

with no independent variables.  And let's assume that there are 2 observations for each participant.  In equation form, this model is:

y_ij = mu + u_i + eps_ij, where i indexes participants, j = 1,2 indexes observations.  The standard assumptions are the u_i ~ N(0, sig_u), eps_ij ~ N(0, sig_e), iid.  From this, we can deduce that y_i1 and y_i2 have a joint bivariate normal distribution with mean mu and variance V = sig_u^2 + sig_e^2, and correlation r = sig_u^2/(sig_u^2 + sig_e^2).