Graphical Models for Associations between Variables, some of which are Qualitative and some Quantitative

by: Steffen L Lauritzen, Nanny Wermuth

Annals of Statistics, Vol. 17, No. 1. (1998), pp. 31-57.

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Abstract

We define and investigate classes of statistical models for the analysis of associations between variables, some of which are qualitative and some quantitative. In the cases where only one kind of variables is present, the models are well-known models for either contingency tables or covariance structures. We characterize the subclass of decomposable models where the statistical theory is especially simple. All models can be represented by a graph with one vertex for each variable. The vertices are possibly connected with arrows or lines corresponding to directional or symmetric associations being present. Pairs of vertices that are not connected are conditionally independent given some of the remaining variables according to specific rules.

@article{lauritzen1989graphicalmodels, abstract = {We define and investigate classes of statistical models for the analysis of associations between variables, some of which are qualitative and some quantitative. In the cases where only one kind of variables is present, the models are well-known models for either contingency tables or covariance structures. We characterize the subclass of decomposable models where the statistical theory is especially simple. All models can be represented by a graph with one vertex for each variable. The vertices are possibly connected with arrows or lines corresponding to directional or symmetric associations being present. Pairs of vertices that are not connected are conditionally independent given some of the remaining variables according to specific rules.}, author = {Lauritzen, Steffen L. and Wermuth, Nanny }, citeulike-article-id = {2969685}, doi = {http://dx.doi.org/doi:10.1214/aos/1176347003}, journal = {Annals of Statistics}, keywords = {graphical\_model}, number = {1}, pages = {31--57}, posted-at = {2008-07-07 13:55:58}, priority = {2}, title = {Graphical Models for Associations between Variables, some of which are Qualitative and some Quantitative}, url = {http://dx.doi.org/doi:10.1214/aos/1176347003}, volume = {17}, year = {1998} }

RIS record

TY - JOUR ID - lauritzen1989graphicalmodels L3 - citeulike-article-id:2969685 TI - Graphical Models for Associations between Variables, some of which are Qualitative and some Quantitative JF - Annals of Statistics VL - 17 IS - 1 SP - 31 EP - 57 N2 - We define and investigate classes of statistical models for the analysis of associations between variables, some of which are qualitative and some quantitative. In the cases where only one kind of variables is present, the models are well-known models for either contingency tables or covariance structures. We characterize the subclass of decomposable models where the statistical theory is especially simple. All models can be represented by a graph with one vertex for each variable. The vertices are possibly connected with arrows or lines corresponding to directional or symmetric associations being present. Pairs of vertices that are not connected are conditionally independent given some of the remaining variables according to specific rules. KW - graphical_model AU - Lauritzen, Steffen AU - Wermuth, Nanny PY - 1998/// UR - http://dx.doi.org/doi:10.1214/aos/1176347003 ER -

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