Theoretical and Practical Comparison of Weights-of-Evidence and Logistic Regression Models Based on the Notion of Markov Random Fields.

@inproceedings{SchaebenGM2013,
 abstract = { A mathematical view of potential modeling is presented in terms of generalized linear models, graphical models and Markov random fields. For example, the global Markov property of a graphical model establishes an immediate relationship of a graph property, separation of nodes, to a statistical property, conditional independence of random variables. Moreover both Markov properties of stochastic graphs and conditional independence are related to factorization of joint probabilities, which in turn often simplifies estimation of probabilities. Thus graphical models provide the means to represent and manage stochastic dependence including conditional stochastic independence. Then it is applied to discuss weights-of-evidence and logistic regression models, and to relate both approaches to log-linear models. While weights-of-evidence and logistic regression model conditional probabilities of an indicator random variable, the subject of generalized models is the joint probability of random variables. Referring to log-linear models provides a test of conditional stochastic independence. Then weights-of-evidence, logistic regression without interaction terms, and logistic regression including interaction terms can be put into a hierarchy of methods, where each former method is a special case of the consecutive latter method. Logistic regression is less restrictive than weights-of-evidence, accounts for violation of conditional independence exactly by corresponding interaction terms, and is optimum for discrete, binary or categorical, predictor variables. Our theoretical findings are completed by a practical example applying weights-of-evidence and logistic regression with R from within gOcad to a gOcad geomodel in voxset mode. },
 author = { Schaeben, Helmut AND Schmidt, Sabine },
 booktitle = { Proc. 33rd Gocad Meeting, Nancy },
 title = { Theoretical and Practical Comparison of Weights-of-Evidence and Logistic Regression Models Based on the Notion of Markov Random Fields. },
 year = { 2013 }
}