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Count Data Models of Prescribed Fire Escapes

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We specify several count data models, parameterizing the probability densities in terms of their means for easier comparison between models. In addition, we derived a correction of these probability densities for differences in sample sizes, which is a contribution to the count data literature as far as we are aware. We then empirically implement these models using data from a mail survey of firms using prescribed fire to estimate the expected number of escapes from prescribed burns. We find that the not correcting for sample size differences can lead to erroneous conclusions concerning the statistical significance of variables.
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... This result is consistent with prescribed fires reducing future risk in a manner that maximizes a net welfare criterion. Mitchell, et al., (2009) analyze prescribed fire escapes and liability law in the United States. When a prescribed fire is used and it escapes its bounds, it is then considered escaped, becomes a wildfire, and suppression efforts are used. ...
... escapes and liability law in the United States. When a prescribed fire is used and it escapes its bounds, it is then considered escaped, becomes a wildfire, and suppression efforts are used. According to current liability law the person, or group, that sets the prescribed fire that escapes is liable for any and all damage occurring from said fire (Mitchell, et. al., 2009). Mitchell, et al., use a count data model, specifically a hurdle model, to predict prescribed fire escapes. ...
... The CATI software was programmed to include edit checks to detect illegal values and logic errors as responses were entered into the computer during the interview. Data Analysis The written survey data were analyzed to predict the number of escapes using several count data models including Poisson, negative binomial and single-parameter count data models (Mitchell et al. 2006). The telephone data were analyzed to estimate the probability and magnitude of property damage resulting from the escaped fire. ...
... The written survey data were analyzed to predict the number of escapes using several count data models including Poisson, negative binomial and single-parameter count data models (Mitchell et al. 2006). The telephone data were analyzed to estimate the probability and magnitude of property damage resulting from the escaped fire. ...
... where is the mean of s, is the scale parameter and the variance is (1 + ) 2 . 54,55 To estimate the impact of various factors on the expected number of sites of action used, regression analysis uses an exponential link function = exp( ′ Z), where is a vector of coefficients to estimate and Z is a vector of covariates that may affect such as the use of HR seed or the field being in an atrazine PA. Finally, because the model simplifies to the standard Poisson density when = 0, the specification can be tested using the significance of this parameter. ...
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