Context-specific independencies in stratified chain regression graphical models
Graphical models are used in multivariate analysis to provide an intuitive visualization of the dependencies among variables, and to easily define a parametrization of the underlying statistical model. Working with categorical variables, the number of model parameters is usually large even in relatively simple graphical models, leading to some difficulties in their interpretation and to some numerical issues in estimation. This paper addresses this issue in a special case where independence between sets of variables holds for particular values of the conditioning variables. This is named as ``context-specific independence''. To encode such an independence in the model parametrization leads to a more parsimonious parametrization, and therefore simplifies both the interpretation and the computation. The theoretical results on the parametrization lead to a learning procedure to actually estimate the model parameters. An application to a dataset on the Italian survey on the effect of innovation in small and medium enterprises is discussed in the final section. It shows the usefulness and the practical applicability of the proposed methodology.
scientific article; zbMATH DE number 7370739
scientific article