We extend the log-mean linear parameterization for binary data to discrete variables with arbitrary number of levels and show that also in this case it can be used to parameterize bi-directed graph models. Furthermore, we show that the log-mean linear parameterization allows one to simultaneously represent marginal independencies among variables and marginal independencies that only appear when certain levels are collapsed into a single one. We illustrate the application of this property by means of an example based on genetic association studies involving single-nucleotide polymorphisms. More generally, this feature provides a natural way to reduce the parameter count, while preserving the independence structure, by means of substantive constraints that give additional insight into the association structure of the variables.

Log-mean linear parameterization for discrete graphical models of marginal independence and the analysis of dichotomizations

ROVERATO, ALBERTO
2015

Abstract

We extend the log-mean linear parameterization for binary data to discrete variables with arbitrary number of levels and show that also in this case it can be used to parameterize bi-directed graph models. Furthermore, we show that the log-mean linear parameterization allows one to simultaneously represent marginal independencies among variables and marginal independencies that only appear when certain levels are collapsed into a single one. We illustrate the application of this property by means of an example based on genetic association studies involving single-nucleotide polymorphisms. More generally, this feature provides a natural way to reduce the parameter count, while preserving the independence structure, by means of substantive constraints that give additional insight into the association structure of the variables.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/384275
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