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Count Data Models of Prescribed Fire Escapes
Abstract and Figures
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. ...
Background:
Controversy has surrounded atrazine due to its susceptibility to leaching and runoff, with regular calls for a ban or restrictions on its use. In the context of a decreasing trend in the percentage of US maize using no-till since 2008, coinciding with the trend of glyphosate-resistant weeds becoming problematic in the Midwestern US, we empirically examine how atrazine use restrictions impacted the diversity of weed management practices used by Wisconsin maize farmers.
Results:
Using survey data from farms inside and outside atrazine prohibition areas, we found that prohibiting atrazine did not directly impact tillage practices, but rather it increased adoption of herbicide-resistant seed, which then increased adoption of conservation tillage systems. We also found that prohibiting atrazine and using herbicide-resistant seed decreased the number of herbicide sites of action used.
Conclusions:
The results indicate that prohibiting atrazine reduced the diversity of weed management practices, which increased the risk of herbicide resistance. Our concern is that a regulatory policy to address one issue (atrazine in groundwater) has induced farmer responses that increase problems with another issue (herbicide-resistant weeds) that longer term will contribute to water quality problems from increased soil erosion and offset the initial benefits.
This paper explores the specification and testing of some modified count data models. These alternatives permit more flexible specification of the data-generating process (dgp) than do familiar count data models (e.g., the Poisson), and provide a natural means for modeling data that are over- or underdispersed by the standards of the basic models. In the cases considered, the familiar forms of the distributions result as parameter-restricted versions of the proposed modified distributions. Accordingly, score tests of the restrictions that use only the easily-computed ML estimates of the standard models are proposed. The tests proposed by Hausman (1978) and White (1982) are also considered. The tests are then applied to count data models estimated using survey microdata on beverage consumption.
Despite a number of significant advances in count data modeling during the last two decades and the growing popularity of
these models in recreation demand analysis, standard count data models are inadequate to address the fast decay process of
the dependent variable and the associated long tail. This article demonstrates how one and two-parameter alternative count
data models can be used to properly model the fast decay process and the associated long tail commonly observed in recreation
demand analysis. Econometric results from an illustrative application suggest satisfactory performance of four of the eight
alternative count data models proposed in this article.