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

Abstract

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 (≥1). 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.

Keywords

Poisson / Negative binomial (NB) / Zero-inflated Poisson (ZIP) / Zero-inflated negative binomial (ZINB) / Poisson hurdle (PH) / Negative binomial hurdle (NBH) / Likelihood ratio test (LRT) / Vuong test

References

[1] Affleck DLR. Poisson mixture models for regression analysis of stand-level mortality. Can J For Res, 2006, 36(11): 2994-3006.

[2] Burnham KP, Anderson DR. Multimodel inference: understanding AIC and BIC in model selection. Sociol Methods Res, 2004, 33: 261-304.

[3] Cameron AC, Trivedi PK. Regression analysis of count data. 1998, Cambridge: Cambridge University Press

[4] Chang Y, Zhu ZL, Bu RC, et al. Predicting fire occurrence patterns with logistic regression in Heilongjiang Province, China. Landsc Ecol, 2013, 28(10): 1989-2004.

[5] Chou YH, Minnich RA, Chase RA. Mapping probability of fire occurrence in San Jacinto Mountains California, USA. Environ Manag, 1993, 17: 129-140.

[6] Erdman D, Jackson L, Sinko A, et al. Zero-inflated Poisson and zero-inflated negative binomial models using the countreg procedure. 2008, Cary: SAS Global Forum, SAS Institute Inc

[7] García Diez EL, Rivas SL, de Pablo F, et al. Prediction of the daily number of forest fires. Int J Wildland Fire, 1999, 9(3): 207-211.

[8] Griffith DA, Haining R. Beyond mule kicks: the Poisson distribution in geographical analysis. Geogr Anal, 2006, 38(2): 123-139.

[9] Guo FT, Hu HQ, Jin S, Ma ZH, Zhang Y. Relationship between forest lighting fire occurrence and weather factors in Daxing’an Mountains based on negative binomial model and zero-inflated negative binomial models. Chin J Plant Ecol, 2010, 34(5): 571-577.

[10] Guo FT, Hu HQ, Ma ZH, et al. Applicability of different models in simulating the relationships between forest fire occurrence and weather factors in Daxing’an Mountains. Chin J Appl Ecol, 2010, 21(1): 159-164.

[11] Hu M, Pavlicova M, Nunes EV. Zero-inflated and hurdle models of count data with extra zeros: examples from an HIV-Risk reduction intervention trial. Am J Drug Alcohol Abuse, 2011, 37(5): 367-375.

[12] Krawchuk MA, Cumming SG, Flannigan MD. Predicted changes in fire weather suggest increases in lightning fire initiation and future area burned in the mixed wood boreal forest. Clim Change, 2009, 92: 82-97.

[13] Lambert D. Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics, 1992, 34: 1-14.

[14] Lee JH, Han G, Fulp WJ, et al. Analysis of overdispersed count data: application to the human papillomavirus infection in men (HIM) study. Epidemiol Infect, 2011, 30: 1-8.

[15] Liu W, Cela J. Count data models in SAS. 2008, SAS Global Forum, Cary, NC: SAS Institute Inc

[16] Mandallaz D, Ye R. Prediction of forest fires with Poisson model. Can J For Res, 1997, 27(10): 1685-1694.

[17] Martell DL, Otukol S, Stocks BJ. A logistic model for predicting daily people-caused forest fire occurrence in Ontario. Can J For Res, 1987, 17: 394-401.

[18] Miaou SP. The relationship between truck accidents and geometric design of road sections: Poisson versus negative binomial regressions. Accid Anal Prev, 1994, 26(4): 471-482.

[19] Mullahy J. Specification and testing of some modified count data models. J Econom, 1986, 33: 341-365.

[20] Numna S (2009) Analysis of extra zero counts using zero-inflated Poisson models. M.Sc. Thesis, Department of Mathematics, Prince of Songkla University, Hat Yai, Songkhla

[21] O’Brien RM. A caution regarding rules of thumb for variance inflation factors. Qual Quant, 2007, 41: 673-690.

[22] Osgood W. Poisson-based regression analysis of aggregate crime rates. J Quant Criminol, 2000, 16(1): 21-43.

[23] Podur JJ, Martell DL, Stanford D. A compound Poisson model for the annual area burned by forest fires in the province of Ontario. Environmetrics, 2009, 21(5): 457-469.

[24] Poulin-Costello M (1993) People-caused forest fire prediction using Poisson and logistic regression. M.Sc. Thesis, Department of Mathematics and Statistics, University of Victoria, Victoria, B.C

[25] Preisler HK, Brillinger DR, Burgan RE, et al. Probability based models for estimation of wildfire risk. Intermt Fire Sci Lab, 2004, 13: 133-142.

[26] Ridout M, Hinde J, Demetrio CG. A score test for testing a zero-inflated Poisson regression model against zero-inflated negative binomial alternatives. Biometrics, 2001, 57(1): 219-223.

[27] Rose CE, Martin SW, Wannemuegler KA, et al. On the use of zero-inflated and hurdle models for modeling vaccine adverse event count data. J Biopharm Stat, 2006, 16(4): 463-481.

[28] R Development Core Team, 2005. R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, www.R-project.org

[29] Vega-Garcia C, Woodard PM, Titus SJ, et al. A logistic model for predicting the daily occurrence of human caused forest fires. Intermt Fire Sci Lab, 1995, 5: 101-111.

[30] Vuong QH. Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica, 1989, 57(2): 307-333.

[31] Xu H. Forests in Daxing’anling mountaions. 1998, Beijing: Science Press

[32] Xu Z (2014) Predicting wildfires and measuring their impacts: case studies in British Columbia. Ph.D. Dissertation, University of Victoria

[33] Yau KKW, Lee AH. Zero-inflated Poisson regression with random effects to evaluate an occupational injury prevention program. Stat Med, 2001, 20(19): 2907-2920.

[34] Yu C, Hu H, Wei R. Dynamic analysis of meteorological conditions of forest fire in Tahe forestry bureau of Daxing’an mountains. J Northeast For Univ, 2007, 35(8): 23-25.