The Annals of Statistics

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

S. L. Lauritzen and N. Wermuth

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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 information

Source
Ann. Statist., Volume 17, Number 1 (1989), 31-57.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347003

Digital Object Identifier
doi:10.1214/aos/1176347003

Mathematical Reviews number (MathSciNet)
MR981437

Zentralblatt MATH identifier
0669.62045

JSTOR
links.jstor.org

Subjects
Primary: 62H99: None of the above, but in this section
Secondary: 62J99: None of the above, but in this section

Keywords
Analysis of variance conditional independence contingency tables covariance selection exponential families logistic regression log-linear models Markov random fields multivariate analysis path analysis regression recursive models triangulated graphs

Citation

Lauritzen, S. L.; Wermuth, N. Graphical Models for Associations between Variables, some of which are Qualitative and some Quantitative. Ann. Statist. 17 (1989), no. 1, 31--57. doi:10.1214/aos/1176347003. https://projecteuclid.org/euclid.aos/1176347003


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Corrections

  • See Correction: S. L. Lauritzen, N. Wermuth. Correction: Graphical Models for Associations Between Variables, Some of which are Qualitative and Some Quantitative. Ann. Statist., Volume 17, Number 4 (1989), 1916--1916.