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st: Random Effects, Fixed Effects, and Population Averaged models?


From   "Anderson, Bradley" <BJAnderson@butler.org>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: Random Effects, Fixed Effects, and Population Averaged models?
Date   Mon, 22 Dec 2008 15:43:27 -0500

Not sure this is an appropriate question for this forum but I'm hoping someone can at least point me to resources.  I'm analyzing data from a clinical trial and have intensive longitudinal data.  Data were collected at baseline and 3 follow-up assessments using time-line follow-back methodology.  There are over 300 discret observations for some subjects.  The primary outcome is dichotomous.  The specific model I'm asking about includes treatment condition (1 if treatment 0 if control), three dummy variables representing the 3 follow-up assessment periods (baseline is coded 0 on all three dummy indicators), and three terms representing the treatment by follow-up period interactions.  If the model is estimated using the random effects logistic regression estimator using xtlogit the treatment by time interaction is statistically signficant.  Using fixed effects logistic regression the treatment by time interaction is statistically signficant.  Population averaged estimates with!
  model based standard errors and either an exchangeable or autoregressive working correlation structure give results consistent with the random effects and fixed effects estimators.  However, if I request the Sandwich robust standard error estimators for the population averaged models the treatment by time interaction is not signficant statistically.  And there are huge differences in the standard errors and associated test statistics between this model and the other 3 models.  FWIW, I've tried a few other models using summary a summary measure of baseline behavior and the follow-up data and some models using linear and quadratic measures of continous time.  I'm getting pretty much the same kind of pattern.  The population average estimates with robust standard errors are very different than the re, fe, or pa with model based standard errors.  The differences make me very uneasy.  How do I resolve these differences in an applied setting?

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