### Citations

64 |
Multivariate logistic models.
- Glonek, McCullagh
- 1995
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Citation Context ...on-linear constraints are used, parsimonious submodels cannot be easily specified. Successively, Lupparelli et al. [5] considered the multivariate logistic parameter η = (ηA)A⊆V of Glonek & McCullagh =-=[4]-=-, defined by the link function η = C logLπ for suitable rectangular matrices C and L, and specified a bidirected graph model by means of the linear constraints ηD = 0, where D varies in the disconnect... |

64 | Markov properties for acyclic directed mixed graphs.
- Richardson
- 2003
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Citation Context ...n Graphical models of marginal independence, introduced by Cox & Wermuth [1] with the name of covariance graph models, are also known in the literature as bidirected graph models following Richardson =-=[6]-=-. These models are of special interest because they belong to the families of ancestral and summary graphs; see Wermuth & Sadeghi [8] for a review. Let G = (V,E) be a bidirected graph defined by a fin... |

60 |
Linear dependencies represented by chain graphs.
- Cox, Wermuth
- 1993
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Citation Context ...dels of marginal independence: a comparison of different approaches Monia Lupparelli and Luca La Rocca 1 Background and notation Graphical models of marginal independence, introduced by Cox & Wermuth =-=[1]-=- with the name of covariance graph models, are also known in the literature as bidirected graph models following Richardson [6]. These models are of special interest because they belong to the familie... |

13 |
Binary Models for Marginal
- Drton, Richardson
- 2005
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Citation Context ... probabilities are obtained as linear functions of the joint probabilities, i.e., µ = Zπ, where Z is a square matrix and is the inverse of the Möbius matrix M such that π = Mµ; see Drton & Richardson =-=[2]-=- for technical details. Choosing a parameterization for graphical models of marginal independence is a crucial task mainly for two reasons: a) pairwise independencies do not imply higher Monia Luppare... |

11 | Marginal log-linear Parameters for Graphical Markov Models.
- Evans, Richardson
- 2013
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Citation Context ...ing higher order LML interactions. We finally obtain a bidirected graph submodel with deviance χ2 (92) = 99.50 (p = 0.279, AIC = −84.5). The same data set has been also analyzed by Evans & Richardson =-=[3]-=- using the multivariate logistic parameterization. These authors find a parsimonious submodel by vanishing all 4-5-6 and 7-way interactions, together with those 3-way interactions that are not signifi... |

11 | Sequences of regressions and their independences.
- Sadeghi, Wermuth
- 2010
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Citation Context ... in the literature as bidirected graph models following Richardson [6]. These models are of special interest because they belong to the families of ancestral and summary graphs; see Wermuth & Sadeghi =-=[8]-=- for a review. Let G = (V,E) be a bidirected graph defined by a finite set V = {1,..., p} of nodes and a symmetric set of edges E ⊆ V ×V drawn as bidirected. Under the pairwise Markov property, for a ... |

10 | Parameterizations and fitting of bi-directed graph models to categorical data. Available at arXiv:0801.1440.
- Lupparelli, Marchetti, et al.
- 2008
(Show Context)
Citation Context ...not have an immediate interpretation in terms of dependence/independence and, since non-linear constraints are used, parsimonious submodels cannot be easily specified. Successively, Lupparelli et al. =-=[5]-=- considered the multivariate logistic parameter η = (ηA)A⊆V of Glonek & McCullagh [4], defined by the link function η = C logLπ for suitable rectangular matrices C and L, and specified a bidirected gr... |

1 |
L.: Log-mean linear models for binary data. Cornell University arXiv:1109.6239v2[stat.ME
- Roverato, Lupparelli, et al.
- 2012
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Citation Context ...ytically available, and classical constrained likelihood maximization, although straightforward, is hampered by the large dimension of the rectangular matrices C and L. More recently, Roverato et al. =-=[7]-=- studied a parameterization based on a log-linear expansion of the parameter µ. The next section shows how this parameterization can be used to define parsimonious bidirected graph submodels.Binary m... |