  The classical multilevel model fails to capture the proximity effect in
epidemiological studies, where subjects are nested within geographical units.
Multilevel Conditional Autoregressive models are alternatives to help explain
the spatial effect better. They have been developed for cross-sectional studies
but not for longitudinal studies so far. This paper has two goals. Firstly, it
further develops the multilevel (growth) models for longitudinal data by adding
existing area level random effect terms with CAR prior specification, whose
structure is changing over time. We name these models MLM tCARs for
longitudinal data. We compare the developed MLM tCARs to the classical
multilevel growth model via simulation studies in common spatial data
situations. The results indicate the better performance of the MLM tCARs, to
retrieve the true regression coefficients and with better fit in general.
  Secondly, this paper provides a comprehensive decision tree for analysing
data in epidemiological studies with spatially nested structure: we also
consider the Multilevel Conditional Autoregressive models for cross-sectional
studies (MLM CARs). We compare three models (for cross-sectional studies) via
simulation studies: the classical multilevel model, the multilevel CAR model
and the Restricted CAR model that accounts for spatial confounding. The MLM
CARs, particularly the Restricted CAR show better results. We apply the models
comparatively on the analysis of the association between greenness and
depressive symptoms in the longitudinal Heinz Nixdorf Recall Study. The results
show negative association between greenness and depression and a decreasing
linear individual time trend for all models. We observe very weak spatial
variation and moderate temporal autocorrelation.
