For a set of variables collected in a contingency table, we focus on a particular kind of relationships such as the context-specific independencies. These are conditional independencies that hold for particular values of the conditioning set. Given the advantages of the graphical models, we use them to represent different relationships among the variables, including the context-specific independencies. In particular, we enrich chain graph models with labelled arcs. Furthermore, we consider the well-known relationships between chain graph models and hierarchical multinomial marginal models and we introduce new constraints on parameters in order to describe the context-specific relationship. Finally, we provide an application to the study of innovation in Italy by comparing two different periods.

Context-Specific independencies embedded in Chain Graph Models of type I / F. Nicolussi, M. Cazzaro (STUDIES IN CLASSIFICATION, DATA ANALYSIS, AND KNOWLEDGE ORGANIZATION). - In: Statistical learning of complex data / Greselin F., Deldossi L.,Bagnato L., Vichi M. ; [a cura di] F. Greselin, L. Deldossi, L. Bagnato, M. Vichi. - [s.l] : Springer, 2019. - ISBN 978-3-030-21139-4. - pp. 173-180 (( Intervento presentato al 11. convegno CLADAG: Biannual meeting of the Classification and Data Analysis Group : 13th - 15th September tenutosi a Milano nel 2017 [10.1007/978-3-030-21140-0].

Context-Specific independencies embedded in Chain Graph Models of type I

F. Nicolussi;
2019

Abstract

For a set of variables collected in a contingency table, we focus on a particular kind of relationships such as the context-specific independencies. These are conditional independencies that hold for particular values of the conditioning set. Given the advantages of the graphical models, we use them to represent different relationships among the variables, including the context-specific independencies. In particular, we enrich chain graph models with labelled arcs. Furthermore, we consider the well-known relationships between chain graph models and hierarchical multinomial marginal models and we introduce new constraints on parameters in order to describe the context-specific relationship. Finally, we provide an application to the study of innovation in Italy by comparing two different periods.
categorical variables; context-specific independencies; ordinal variables; stratified chain graph models;
Settore SECS-S/01 - Statistica
Società italiana di statistica
Book Part (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/709708
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