#### DMCA

## Two algorithms for fitting constrained marginal models (2013)

Venue: | Computational Statistics and Data Analysis |

Citations: | 5 - 1 self |

### Citations

4181 | Regression shrinkage and selection via the lasso
- Tibshirani
- 1996
(Show Context)
Citation Context ... log-likelihood φ(θ) ≡ l(θ)− t−1∑ j=1 νj |ηj(θ)|, for some vector of penalties ν = (νj) ≥ 0. The advantage of penalties of this form is that one can obtain parameter estimates which are exactly zero (=-=Tibshirani, 1996-=-). Setting parameters of the form η to zero corresponds to many interesting submodels, such as those defined by conditional independences, (Forcina et al., 2010, Rudas et al., 2010), we can therefore ... |

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

2947 | Categorical data analysis - Agresti - 2002 |

1214 |
Nonlinear Programming. Athena Scientific
- Bertsekas
- 1999
(Show Context)
Citation Context ...n addition, as a consequence of the Karush-Kuhn-Tucker conditions, if a local maximum of the constrained objective function exists, then it will be a saddle point of the Lagrangian (see, for example, =-=Bertsekas, 1999-=-). To ensure that the stationary point reached by the algorithm is indeed a local maximum of the original problem, one could look at the eigenvalues of the observed information with respect to β: if t... |

719 | Regularization paths for generalized linear models via coordinate descent
- Friedman
- 2010
(Show Context)
Citation Context ... |ηj| with respect to ηj , with η1, . . . , ηj−1, ηj+1, . . . , ηt−1 held fixed. This is solved just by taking ηj = sign(η̌)(|η̌| − νj)+, where a+ = max{a, 0}, and η̌j minimizes Q with respect to ηj (=-=Friedman et al., 2010-=-). This approach to the sub-problem may require a large number of iterations, but it is extremely fast in practice because each step is so simple. If the overall algorithm converges, then by a similar... |

97 | Multivariate regression analyses for categorical data. - KY, SL, et al. - 1992 |

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

52 | Simultaneously modeling joint and marginal distributions of multivariate categorical responses. - Lang, Agresti - 1994 |

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

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

17 | Marginal regression models for the analysis of positive association of ordinal response variables. - Colombi, Forcina - 2001 |

16 | An extended class of marginal link functions for modelling contingency tables by equality and inequality constraints - Bartolucci, Colombi, et al. |

11 | Marginal log-linear Parameters for Graphical Markov Models.
- Evans, Richardson
- 2013
(Show Context)
Citation Context ...of this family of parameterizations enables their application to many popular classes of conditional independence models, and especially to graphical models (Forcina et al., 2010, Rudas et al., 2010, =-=Evans and Richardson, 2011-=-). Bergsma and Rudas (2002) show that, under certain conditions, models defined by linear constraints on MLLPs are curved exponential families. However, näıve algorithms for maximum likelihood estima... |

7 | Marginal log-linear parameterization of conditional independence models. - Rudas, Bergsma, et al. - 2010 |

2 | Stochastic monotonicity in intergenerational mobility tables - Dardanoni, Fiorini, et al. |

1 | Parametrizations of discrete graphical models - Evans - 2011 |

1 | Relational models for contingency tables. arXiv:1102.5390 - Klimova, Rudas, et al. - 2011 |