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## Log-mean linear models for binary data (2013)

Venue: | Biometrika |

Citations: | 3 - 2 self |

### Citations

3163 | Generalized Linear Models. - McCullagh, Nelder - 1989 |

2947 |
Categorical data analysis
- Agresti
- 2002
(Show Context)
Citation Context ...h that sub-models of interest correspond to linear subspaces of the parameter space of the saturated model. Log-linear parameters are computed as a log-linear expansion of the cell probabilities (see =-=Agresti, 2002-=-) and can be seen as a special case of the wider family of marginal log-linear parameters of Bergsma and Rudas (2002). These parameters are defined by first specifying a suitable sequence of marginal ... |

1584 |
Graphical Models
- Lauritzen
- 1996
(Show Context)
Citation Context ...sed to define the class of log-linear models, which is widely used for the analysis of discrete data (see Agresti, 2002) and includes, as a special case, the class of undirected graphical models (see =-=Lauritzen, 1996-=-, Chap. 4). The mean parameter of the multivariate Bernoulli distribution is µ = (µD)D⊆V , where µ∅ = 1 (on grounds of convention) and µD = P (XD = 1D) otherwise. This was 5 called the Möbius paramet... |

800 | Constrained Optimization and Lagrange Multiplier Methods - Bertsekas - 1982 |

309 | A simulation study of the number of events per variable in logistic regression analysis. - Peduzzi, Concato, et al. - 1996 |

140 | Multivariate dependencies: Models, analysis and interpretation. - Cox, Wermuth - 1996 |

138 |
Conditional independence in statistical theory (with discussion
- Dawid
- 1979
(Show Context)
Citation Context ...amily of probability distributions for XV that satisfy a given Markov property with respect to a bidirected graph G. Given three disjoint subsets A,B,C ⊆ V , we use the standard notation XA⊥⊥XB | XC (=-=Dawid, 1979-=-) to represent the statement “XA is independent of XB given XC”. The distribution of XV satisfies the pairwise Markov property if, for every missing edge jk, it holds that Xj ⊥⊥Xk. The distribution of... |

85 | Maximum Likelihood Estimation of Parameters Subject to Constraint - AITCHISON, J, et al. - 1958 |

64 | Multivariate logistic models. - Glonek, McCullagh - 1995 |

64 | Markov properties for acyclic directed mixed graphs.
- Richardson
- 2003
(Show Context)
Citation Context ...f XB given XC”. The distribution of XV satisfies the pairwise Markov property if, for every missing edge jk, it holds that Xj ⊥⊥Xk. The distribution of XV satisfies the connected set Markov property (=-=Richardson, 2003-=-) if, for every disconnected set D, the subvectors corresponding to its connected components XC1 , . . . , XCr are mutually independent. For instance, in the bidirected graph of Figure 1, the set {1, ... |

60 | Linear dependencies represented by chain graphs. - Cox, Wermuth - 1993 |

51 | Marginal models for categorical data. - Bergsma, Rudas - 2002 |

37 | Discrete chain graph models. - Drton - 2009 |

25 | Binary models for marginal independence. - Drton, Richardson - 2008 |

24 | Premature age-related comorbidities among HIV-infected persons compared with the general population,” - Guaraldi, Orlando, et al. - 2011 |

22 | Marginal regression analysis of a multivariate binary response - Ekholm, Smith, et al. - 1995 |

20 | Additive and multiplicative models and interactions - Darroch, Speed - 1983 |

18 | Maximum likelihood methods for a generalized class of log-linear models. - Lang - 1996 |

18 | Chain graph models of multivariate regression type for categorical data. Bernoulli,
- Marchetti, Lupparelli
- 2010
(Show Context)
Citation Context ...ral contexts (see Bergsma et al., 2009) and, in particular, they have been recently used for different types of graphical models of marginal independence (Lupparelli et al., 2009; Rudas et al., 2010; =-=Marchetti and Lupparelli, 2011-=-; Evans and Richardson, 2011). A disadvantage of marginal log-linear parameterizations is that their inverse mappings cannot be analytically computed (but for the special case of λ). 2.2 Marginal inde... |

17 | Statistical inference in context specific interaction models for contingency tables. Scand Stat - Højsgaard - 2004 |

17 | Cumulative distribution networks and the derivative-sum-product algorithm: Models and inference for cumulative distribution functions on graphs - Huang, Frey - 2011 |

15 | Model search among multiplicative models - Wermuth - 1976 |

14 | Sample size for logistic regression with small response probability’, - Whittemore - 1981 |

13 | Association models for a multivariate binary response - Ekholm, McDonald, et al. - 2000 |

13 | Global systems biology, personalized medicine and molecular epidemiology,” - Nicholson - 2006 |

11 |
Marginal models: For dependent, clustered, and longitudinal categorial data
- Bergsma, Croon, et al.
- 2009
(Show Context)
Citation Context ..., and it is typically used for modelling marginal distributions; see McCullagh and Nelder (1989, Chap. 6). More generally, marginal log-linear parameterizations can be useful in several contexts (see =-=Bergsma et al., 2009-=-) and, in particular, they have been recently used for different types of graphical models of marginal independence (Lupparelli et al., 2009; Rudas et al., 2010; Marchetti and Lupparelli, 2011; Evans ... |

11 | Marginal log-linear Parameters for Graphical Markov Models.
- Evans, Richardson
- 2013
(Show Context)
Citation Context ..., 2009) and, in particular, they have been recently used for different types of graphical models of marginal independence (Lupparelli et al., 2009; Rudas et al., 2010; Marchetti and Lupparelli, 2011; =-=Evans and Richardson, 2011-=-). A disadvantage of marginal log-linear parameterizations is that their inverse mappings cannot be analytically computed (but for the special case of λ). 2.2 Marginal independence and bidirected grap... |

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 ...inear parameterizations can be useful in several contexts (see Bergsma et al., 2009) and, in particular, they have been recently used for different types of graphical models of marginal independence (=-=Lupparelli et al., 2009-=-; Rudas et al., 2010; Marchetti and Lupparelli, 2011; Evans and Richardson, 2011). A disadvantage of marginal log-linear parameterizations is that their inverse mappings cannot be analytically compute... |

9 | A factorization criterion for acyclic directed mixed graphs - Richardson |

8 | Marginal log-linear models for categorical data - Bergsma, Rudas - 2002 |

7 | Marginal log-linear parameterization of conditional independence models.
- Rudas, Bergsma, et al.
- 2010
(Show Context)
Citation Context ...an be useful in several contexts (see Bergsma et al., 2009) and, in particular, they have been recently used for different types of graphical models of marginal independence (Lupparelli et al., 2009; =-=Rudas et al., 2010-=-; Marchetti and Lupparelli, 2011; Evans and Richardson, 2011). A disadvantage of marginal log-linear parameterizations is that their inverse mappings cannot be analytically computed (but for the speci... |

5 | Two algorithms for fitting constrained marginal models - Evans, Forcina - 2013 |

5 | Marginal parameterizations of discrete models defined by a set of conditional independencies - Forcina, Lupparelli, et al. - 2010 |

4 | The Marke-Nyman temperament scale: an English translation - Coppen |