Re: st: baseline adjustment in linear mixed models

[Clyde B Schechter <clyde.schechter@einstein.yu.edu>]

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).