The discriminatory ability of postfire tree mortality logistic regression models

Abstract

Western land managers desire a method to discriminate between individual live and dead trees to support postfire management decisions such as salvage logging. Logistic regression models have been suggested for this purpose following prescribed fire and wildfire for ponderosa pine (Pinus ponderosa Dougl. Ex Laws.). Goodness of fit of the regression model is not sufficient for good discrimination. We demonstrate methods to evaluate discriminatory ability using six previously published logistic models and five data sets of postfire tree mortality. The area under the receiver operating characteristic curve (AUC) provides an average assessment of discriminatory ability over all false positive and false negative error rates. In management settings, it may be important to assess correct prediction rates for a maximum false positive rate rather than averaged over all false positive rates. Therefore, we suggest an additional statistic, CP|FP D, the correct prediction rate for a fixed false positive rate, D. Both goodness of fit and discriminatory ability should be assessed to insure accurate discrimination. We further suggest that the sampling variation of the AUC and CP|FP D statistics be small and that distributions be centered on values that are acceptable to practitioners.