ABSTRACT
Bayesian Hierarchical Models
10.1 Introduction to Hierarchical Models
Hierarchical data is regularly encountered in the social and behavioral sci-
ences since measurement often takes place at dierent levels of aggregation.
For instance, in a sociological survey analysis, we might augment the col-
lected data from individuals with historical, geographic, or economic vari-
ables measured at various geographic levels. The question then arises as to
how we should treat the dierent levels of variables in the same statistical
model. Ignoring the aggregate information excludes potentially important
eects and treating the aggregate information as individual level eects
confuses covariance in the model. The solution is to employ a hierarchical
model that recognizes the dierent groupings or time points that informa-
tion about individual observations occur, thereby specically stipulating
correlations that would not have otherwise been assumed to exist. An-
other common justication for specifying hierarchical models is that some
distributional forms cannot adequately account for overdispersion in the
outcome variable of interest (Cox 1983).
