A cautionary note on inference for marginal regression models with longitudinal data and general correlated response data

Inference for cross-sectional models using longitudinal data, can be accomplished with generalized estimating equations (Zeger and Liang, 1992). We show that either a diagonal working covariance matrix should be used or a key assumption should be verified. The assumption is non-trivial when covariates vary over time. The validity of this assumption is explored for some broad classes of correlation structures. Similar considerations are shown to be relevant for the more general problem of correlated response data and marginal regression analysis with individual level covariates.