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ISPRS Int. J. Geo-Inf. 2014, 3(4), 1387-1411; doi:10.3390/ijgi3041387

Targeting: Logistic Regression, Special Cases and Extensions

Institute of Geophysics and Geoinformatics, Technische Universität Bergakademie Freiberg, Gustav-Zeuner-Str. 12, Freiberg 09596, Germany
Received: 10 October 2014 / Revised: 25 November 2014 / Accepted: 25 November 2014 / Published: 11 December 2014
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Abstract

Logistic regression is a classical linear model for logit-transformed conditional probabilities of a binary target variable. It recovers the true conditional probabilities if the joint distribution of predictors and the target is of log-linear form. Weights-of-evidence is an ordinary logistic regression with parameters equal to the differences of the weights of evidence if all predictor variables are discrete and conditionally independent given the target variable. The hypothesis of conditional independence can be tested in terms of log-linear models. If the assumption of conditional independence is violated, the application of weights-of-evidence does not only corrupt the predicted conditional probabilities, but also their rank transform. Logistic regression models, including the interaction terms, can account for the lack of conditional independence, appropriate interaction terms compensate exactly for violations of conditional independence. Multilayer artificial neural nets may be seen as nested regression-like models, with some sigmoidal activation function. Most often, the logistic function is used as the activation function. If the net topology, i.e., its control, is sufficiently versatile to mimic interaction terms, artificial neural nets are able to account for violations of conditional independence and yield very similar results. Weights-of-evidence cannot reasonably include interaction terms; subsequent modifications of the weights, as often suggested, cannot emulate the effect of interaction terms. View Full-Text
Keywords: prospectivity modeling; potential modeling; conditional independence; naive Bayes model; Bayes factors; weights of evidence; artificial neural nets; imbalanced datasets; balancing prospectivity modeling; potential modeling; conditional independence; naive Bayes model; Bayes factors; weights of evidence; artificial neural nets; imbalanced datasets; balancing
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Schaeben, H. Targeting: Logistic Regression, Special Cases and Extensions. ISPRS Int. J. Geo-Inf. 2014, 3, 1387-1411.

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