where lambda hat is the expected annual tropical cyclone rate, NAO, SOI, and SST are the covariates, and the alphas are the model parameters estimated using the method of maximum likelihoods. In the parlance of generalized linear models, the logarithm is the link function.
The reduction in deviance (analogous to the percentage of variance explained in an ordinary least-squares regression) from a model with no covariates ranges from 40% using data back to 1900 to 48% using data back only to 1944. It needs to be emphasized that a Poisson regression is not the same as a normal regression on the logarithm of counts. With Poisson regression you cannot explain all the variation in the data; there will be unexplainable variation due to the stochastic nature of the model. Thus, given that the counts follow a Poisson distribution (excellent assumption), even if the model precisely predicts the rate, the counts will have a degree of variability that cannot be reduced by the model (this is what is called aleatory uncertainty).
Signs on the coefficient estimates are consistent with the theory indicating more disturbances reaching tropical cyclone intensity with greater ocean heat content (positive on the SST coefficient estimate), more cyclone intensification with less shear (positive on the SOI estimate indicating La Nina conditions), and a greater number of cyclones reaching tropical cyclone intensity with a weaker pre-season NAO indicating a preference for storms to remain in the deep tropics (e.g., hurricanes Dean and Felix over the Caribbean Sea during 2007).
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