A Nonsymmetric Logit Model and Grouped Predictand Category Development

Bob Glahn NOAA/National Weather Service/Office of Science and Technology/Meteorological Development Laboratory, Silver Spring, Maryland

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Abstract

Logistic regression is an alternative to regression estimation of event probabilities (REEP) and other techniques for estimating weather event probabilities based on NWP output or other predictors. Logistic regression has the advantage over REEP in that the probability estimates are constrained between zero and unity, whereas REEP can “overshoot” these values. It may be a detriment in some applications that the curves developed, one for each of several predictand categories (events), are symmetric. This paper shows how the logit curve can easily be made nonsymmetric as a function of a predictor, and thereby possibly achieve a better fit to the data. As with REEP, the probabilities estimated by logistic regression for each of several categories of a variable may not be consistent. For instance, the probability of snow > 2 in. may exceed the probability of snow > 1 in. Such inconsistencies can be avoided by developing a single equation involving all predictand categories and including another predictor that is a function of the predictand. This effectively, for a single predictor, produces parallel curves separated along the predictor axis but imposes restrictions on the equations and probabilities produced from them. The relationship between the predictor(s) and the predictand must be considered in determining the functional form. With only one predictor, defining the function is relatively straightforward. However, with multiple predictors, the process is more problematic. This paper demonstrates an alternative to imposing a functional form by using binary predictors. This formulation also achieves the goal of producing consistent forecasts and generalizes more readily to multiple predictors.

Corresponding author address: Bob Glahn, Scientist Emeritus, Meteorological Development Laboratory, NOAA/NWS, 1325 East-West Highway, Silver Spring, MD 20910. E-mail: harry.glahn@noaa.gov

Abstract

Logistic regression is an alternative to regression estimation of event probabilities (REEP) and other techniques for estimating weather event probabilities based on NWP output or other predictors. Logistic regression has the advantage over REEP in that the probability estimates are constrained between zero and unity, whereas REEP can “overshoot” these values. It may be a detriment in some applications that the curves developed, one for each of several predictand categories (events), are symmetric. This paper shows how the logit curve can easily be made nonsymmetric as a function of a predictor, and thereby possibly achieve a better fit to the data. As with REEP, the probabilities estimated by logistic regression for each of several categories of a variable may not be consistent. For instance, the probability of snow > 2 in. may exceed the probability of snow > 1 in. Such inconsistencies can be avoided by developing a single equation involving all predictand categories and including another predictor that is a function of the predictand. This effectively, for a single predictor, produces parallel curves separated along the predictor axis but imposes restrictions on the equations and probabilities produced from them. The relationship between the predictor(s) and the predictand must be considered in determining the functional form. With only one predictor, defining the function is relatively straightforward. However, with multiple predictors, the process is more problematic. This paper demonstrates an alternative to imposing a functional form by using binary predictors. This formulation also achieves the goal of producing consistent forecasts and generalizes more readily to multiple predictors.

Corresponding author address: Bob Glahn, Scientist Emeritus, Meteorological Development Laboratory, NOAA/NWS, 1325 East-West Highway, Silver Spring, MD 20910. E-mail: harry.glahn@noaa.gov
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