Extending Extended Logistic Regression: Extended versus Separate versus Ordered versus Censored

Jakob W. Messner Institute of Meteorology and Geophysics, University of Innsbruck, Innsbruck, Austria

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Georg J. Mayr Institute of Meteorology and Geophysics, University of Innsbruck, Innsbruck, Austria

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Daniel S. Wilks Department of Earth and Atmospheric Sciences, Cornell University, Ithaca, New York

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Achim Zeileis Department of Statistics, Faculty of Economics and Statistics, University of Innsbruck, Innsbruck, Austria

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Abstract

Extended logistic regression is a recent ensemble calibration method that extends logistic regression to provide full continuous probability distribution forecasts. It assumes conditional logistic distributions for the (transformed) predictand and fits these using selected predictand category probabilities. In this study extended logistic regression is compared to the closely related ordered and censored logistic regression models. Ordered logistic regression avoids the logistic distribution assumption but does not yield full probability distribution forecasts, whereas censored regression directly fits the full conditional predictive distributions. The performance of these and other ensemble postprocessing methods is tested on wind speed and precipitation data from several European locations and ensemble forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF). Ordered logistic regression performed similarly to extended logistic regression for probability forecasts of discrete categories whereas full predictive distributions were better predicted by censored regression.

Denotes Open Access content.

Corresponding author address: Jakob W. Messner, Institute of Meteorology and Geophysics, University of Innsbruck, Innrain 52f, 6020 Innsbruck, Austria. E-mail: jakob.messner@uibk.ac.at

Abstract

Extended logistic regression is a recent ensemble calibration method that extends logistic regression to provide full continuous probability distribution forecasts. It assumes conditional logistic distributions for the (transformed) predictand and fits these using selected predictand category probabilities. In this study extended logistic regression is compared to the closely related ordered and censored logistic regression models. Ordered logistic regression avoids the logistic distribution assumption but does not yield full probability distribution forecasts, whereas censored regression directly fits the full conditional predictive distributions. The performance of these and other ensemble postprocessing methods is tested on wind speed and precipitation data from several European locations and ensemble forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF). Ordered logistic regression performed similarly to extended logistic regression for probability forecasts of discrete categories whereas full predictive distributions were better predicted by censored regression.

Denotes Open Access content.

Corresponding author address: Jakob W. Messner, Institute of Meteorology and Geophysics, University of Innsbruck, Innrain 52f, 6020 Innsbruck, Austria. E-mail: jakob.messner@uibk.ac.at
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