Inequality Constrained Multilevel Models
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by
Bernet S. Kato, Carel F.W. Peeters
2018
Abstract
Multilevel or hierarchical data structures can occur in many areas of
research, including economics, psychology, sociology, agriculture, medicine,
and public health. Over the last 25 years, there has been increasing interest
in developing suitable techniques for the statistical analysis of multilevel
data, and this has resulted in a broad class of models known under the generic
name of multilevel models. Generally, multilevel models are useful for
exploring how relationships vary across higher-level units taking into account
the within and between cluster variations. Research scientists often have
substantive theories in mind when evaluating data with statistical models.
Substantive theories often involve inequality constraints among the parameters
to translate a theory into a model. This chapter shows how the inequality
constrained multilevel linear model can be given a Bayesian formulation, how
the model parameters can be estimated using a so-called augmented Gibbs
sampler, and how posterior probabilities can be computed to assist the
researcher in model selection.
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