The main advantage of longitudinal studies is that they can distinguish changes over time within individuals (longitudinal effects) from differences among subjects at the Start of the study (cross-sectional effects). In observational studies, however, longitudinal changes need to be studied after correction for potential important cross-sectional differences between subjects. It will be shown that, in the context of linear mixed models, the estimation of longitudinal effects may be highly influenced by the assumptions about cross-sectional effects. Furthermore, aspects from conditional and mixture inference will be combined, yielding so-called conditional linear mixed models that allow estimation of longitudinal effects (average trends as well as subject-specific trends), independent of any cross-sectional assumptions. These models will be introduced and justified, and extensively illustrated in the analysis of longitudinal data from 680 participants in the Baltimore Longitudinal Study of Aging.