## A Note on Multivariate Logistic Models for Contingency Tables (1997)

Venue: | Austral. J. Statist |

Citations: | 3 - 0 self |

### BibTeX

@ARTICLE{Kauermann97anote,

author = {Göran Kauermann},

title = {A Note on Multivariate Logistic Models for Contingency Tables},

journal = {Austral. J. Statist},

year = {1997},

volume = {39},

pages = {261--276}

}

### OpenURL

### Abstract

Log-linear models are a widely accepted tool for modeling discrete data given in a contingency table. Although their parameters reflect the interaction structure in the joint distribution of all variables, they do not give information about structures appearing in the margins of the table. This is in contrast to multivariate logistic parameters recently introduced by Glonek & McCullagh (1995). They have as parameters the highest order log odds ratios derived from the joint table and from each marginal table. The link between the cell probabilities and the multivariate logistic parameters is given in Glonek & McCullagh in an algebraic fashion. In this paper we focus on this link, showing that it is derived by general parameter transformations in exponential families. In particular, the connection between the natural, the expectation and the mixed parameterization in exponential families (Barndorff-Nielsen, 1978) is used. This also yields the derivatives of the likelihood equation and shows properties of the Fisher matrix. Further emphasis is paid to the analysis of independence hypotheses in margins of a contingency table.