272 adding another variable to the model. Here, this cost is defined as the model variance (i.e., how well the model fits the data). By pruning the subsequent models to a set complexity parame- ter, researchers reduced the number of variables while maintaining variance. As such, the follow- ing list of models provides the variables that were inputs into the recursive partitioning. Resulting models were pruned to a complexity parameter of 0.02 and may not have included all input vari- ables. The initial model included all variables as inputs (ModelA excluding dieback and vigor (both of which require additional training for technicians to pro- duce data within quality control standards, Mod- elC ing only ten- or five-year growth and variation data (ModelE only species and DBH (ModelG ing signs and symptoms with ModelG and ModelF in a management database (species, DBH, and growth rates, ModelD ); including only data that may already exist ; Roman et al. 2013); includ- , respectively); including ). ); and includ- (ModelH Decision Model Assessment Decision models produced in the development phase resulted in probabilities of mortality. Fol- lowing each of the resulting model branching, probabilities of mortality were assigned to each model assessment tree, which were then com- pared using a t-test for each model between trees that survived and those that died during the study period. Additionally, probabilities were convert- ed to categorical data (0,1 predicted survival, mortality) with trees >0.65 probability of mor- tality categorized as dead. Akaike information criterion (AIC) was calculated for each model using binomial likelihood function to identify goodness of model fit for assessment trees. AIC allows for comparison of models, with lower AIC typically indicating a better model, which is influenced by the number of variables included (i.e., increase in variables leads to an increase in AIC) and error (i.e., increase in error leads to an increase in AIC). Those models with the best fit (i.e., low AIC and high percent correct prediction) were used to select variables to pre- dict mortality year (1–3 after initial assessment). ©2015 International Society of Arboriculture oped with the inclusion and exclusion of selected variables, including: excluding dieback (ModelB ). Subsequent models were devel- ); Clark et al.: Ash Mortality Model Development Mortality Year Model Using the decision criteria from the top three models (combination of greatest correct predic- tion and lowest AIC), a mortality year model was produced to identify the effectiveness of predicting a specific mortality year within the study period. Variables used as input to the re- cursive partitioning were those that occurred in the top three decision models. In both develop- ment and assessment, only those trees that died were used. As with the other model assessments, percent correct prediction was used to assist in identifying the goodness of model fit. Analysis of variance was used to compare the predicted mor- tality year between actual mortality years with Tukey’s HSD as a post-hoc test. Statistical analysis was conducted using the base package in R. RESULTS Decision Model Development Of the trees selected for model development, 12 trees were dead in Year1 Year3 . Trees that died were significantly larger and , 54 in Year2 with more crown dieback than trees that survived (Table 1). While the median bark roughness for both live and dead trees was the same as the overall median (2, Table 1), 68.1% of dead trees and 38.9% of live trees had bark rougher than that median. The overall median vigor was 1, with 76.8% of dead trees and 12.9% of live trees in poorer health than the median. Finally, displayed signs of emer- ald ash borer attack was not independent of tree mortality, with trees that died having a greater pro- portion of at least one sign (e.g., bark splits, exit holes, epicormic sprouting, woodpecker activity). Eight decision models were produced from for trees in Michigan and Indiana (Figure 1; Fig- ure 2). ModelC the tree assessment data collected in Year0 and ModelH decision models. ModelD and ModelG resulted in identical included additional variables as inputs, but only DBH was included aſter pruning to a complexity parameter of 0.02. Because these models resulted in identi- cal decisions, they were included for completeness. Decision Model Assessment Of the trees selected for model assessment, 13 trees were dead in Year1 , 50 in Year2 , and 4 in , and 3 in
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