Comparison of six generalized linear models for occurrence of lightning-induced fires in northern Daxing'an Mountains, China

The occurrence of lightning-induced forest fires during a time period is count data featuring over-dispersion (i.e., variance is larger than mean) and a high frequency of zero counts. In this study, we used six generalized linear models to examine the relationship between the occurrence of lightning-induced forest fires and meteorological factors in the Northern Daxing'an Mountains of China. The six models included Poisson, negative binomial (NB), zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), Poisson hurdle (PH), and negative binomial hurdle (NBH) models. Goodness-of-fit was compared and tested among the six models using Akaike information criterion (AIC), sum of squared errors, likelihood ratio test, and Vuong test. The predictive performance of the models was assessed and compared using independent validation data by the data-splitting method. Based on the model AIC, the ZINB model best fitted the fire occurrence data, followed by (in order of smaller AIC) NBH, ZIP, NB, PH, and Poisson models. The ZINB model was also best for predicting either zero counts or positive counts (a parts per thousand yen1). The two Hurdle models (PH and NBH) were better than ZIP, Poisson, and NB models for predicting positive counts, but worse than these three models for predicting zero counts. Thus, the ZINB model was the first choice for modeling the occurrence of lightning-induced forest fires in this study, which implied that the excessive zero counts of lightning-induced fires came from both structure and sampling zeros.