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Marginal loglinear parameters for graphical markov models. arXiv preprint arXiv:1105.6075, 2011. RA Fisher. On the interpretation of χ2 from contingency tables, and the calculation of p
"... Marginal loglinear (MLL) models provide a flexible approach to multivariate discrete data. MLL parametrizations under linear constraints induce a wide variety of models, including models defined by conditional independences. We introduce a subclass of MLL models which correspond to Acyclic Direct ..."
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Cited by 11 (3 self)
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Marginal loglinear (MLL) models provide a flexible approach to multivariate discrete data. MLL parametrizations under linear constraints induce a wide variety of models, including models defined by conditional independences. We introduce a subclass of MLL models which correspond to Acyclic Directed Mixed Graphs (ADMGs) under the usual global Markov property. We characterize for precisely which graphs the resulting parametrization is variation independent. The MLL approach provides the first description of ADMG models in terms of a minimal list of constraints. The parametrization is also easily adapted to sparse modelling techniques, which we illustrate using several examples of real data.
Logmean linear models for binary data
 Biometrika
, 2013
"... This paper is devoted to the theory and application of a novel class of models for binary data, which we call logmean linear (LML) models. The characterizing feature of these models is that they are specified by linear constraints on the LML parameter, defined as a loglinear expansion of the mean ..."
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Cited by 3 (2 self)
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This paper is devoted to the theory and application of a novel class of models for binary data, which we call logmean linear (LML) models. The characterizing feature of these models is that they are specified by linear constraints on the LML parameter, defined as a loglinear expansion of the mean parameter of the multivariate Bernoulli distribution. We show that marginal independence relationships between variables can be specified by setting certain LML interactions to zero and, more specifically, that graphical models of marginal independence are LML models. LML models are code dependent, in the sense that they are not invariant with respect to relabelling of variable values. As a consequence, they allow us to specify submodels defined by codespecific independencies, which are independencies in subpopulations of interest. This special feature of LML models has useful applications. Firstly, it provides a flexible way to specify parsimonious submodels of marginal independence models. The main advantage of this approach concerns the interpretation of the submodel, which is fully characterized by independence relationships, either marginal or codespecific. Secondly, the codespecific nature of these models can be exploited to focus on a fixed, arbitrary, cell of the probability table and on the corresponding subpopulation. This leads to an innovative family of models, which we call pivotal codespecific LML models, that is especially useful when the interest of researchers is focused on a small subpopulation obtained by stratifying individuals according to some features. The application of LML models is illustrated on two datasets, one of which concerns the use of pivotal codespecific LML models in the field of personalized medicine.
Logmean linear models for binary data Alberto
, 2012
"... This paper introduces a novel class of models for binary data, which we call logmean linear models. The characterizing feature of these models is that they are specified by linear constraints on the logmean linear parameter, defined as a loglinear expansion of the mean parameter of the multivaria ..."
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This paper introduces a novel class of models for binary data, which we call logmean linear models. The characterizing feature of these models is that they are specified by linear constraints on the logmean linear parameter, defined as a loglinear expansion of the mean parameter of the multivariate Bernoulli distribution. We show that marginal independence relationships between variables can be specified by setting certain logmean linear interactions to zero and, more specifically, that graphical models of marginal independence are logmean linear models. Our approach overcomes some drawbacks of the existing parameterizations of graphical models of marginal independence.