Arboriculture & Urban Forestry 42(2): March 2016 dependency was not observed in the model residuals, so researchers did not account for spatial autocorrelation in model specification. After the models were constructed, the predicted population at which a community had a 0.5 prob- ability of participating in TCUSA was extracted. It was hypothesized that longer-term TCUSA participants would have larger populations than more recent enrollees. A linear regression model was constructed for TCUSA participants in which log-transformed community popula- tion was the dependent variable, and the year of TCUSA adoption was the independent variable. Based on the hypothesis that larger commu- nities would be longer-term TCUSA partici- pants, an additional linear model was developed that included a quadratic term for the year of TCUSA adoption, as this curve may better cap- ture a potential trend in the data introduced by saturation of TCUSA participation among larger communities. The original linear model was compared to the model with a quadratic term using the Akaike Information Criterion (AIC), where a lower AIC indicates the better model (i.e., the model that more success- fully balances goodness of fit and parsimony). Logistic and linear regression models were constructed in R v3.1.2 (R Core Team 2014). Are TCUSA Participants Spatially Autocorrelated? A join-count statistic was calculated to determine if neighboring communities were more likely to participate in TCUSA than would be expected by random chance. The join-count statistic is a mea- sure of spatial autocorrelation typically calculated using binary data, in this case TCUSA partici- pants (coded 1) and non-participants (coded 0). Using a matrix of candidate community neighbor relationships, the statistic measures the frequency of 1-1, 0-0, and 0-1 joins and compares them to the frequencies expected under a random spa- tial distribution of the same number of 0 and 1 values. For the data set, the join-count statistic was used to evaluate, for each community’s four nearest neighbors, whether TCUSA participants were more likely to be joined than would be ex- pected by chance. In other words, the join-count statistic was used to assess whether TCUSA par- 123 ticipants were spatially autocorrelated. To assess significance, the authors compared the observed join-count statistic to a Monte Carlo simulation with 9,999 randomizations. Join-count statis- tics were calculated in R v3.1.2 (R Core Team 2014) using the spdep package (Bivand 2014). Is TCUSA Participation Related to Socioeconomic Indicators? Logistic regression analyses were conducted to model TCUSA participation as a function of sev- eral socioeconomic variables. In these logistic re- gression models, TCUSA was the binary response variable, and independent variables included the following demographic variables from the 2012 ACS five-year estimate data (U.S. Census Bu- reau 2014): income (median household income), education (high school graduation rate), owner occupancy (percent of housing units occupied by owner), percent white (percent of popula- tion that identifies their race as white alone), age (median population age in years), and total popu- lation. Independent variables were prescreened for excessive collinearity (|r| > 0.7; Dormann et al. 2013); this was not an issue, so all variables were included in the models. Communities with missing data values were excluded from further analysis. Separate models were constructed for each of nine census regions shown in Figure 1. A comprehensive national model was not developed because creation of a national connectivity ma- trix (see below) exceeded computational limits. Inspection of logistic regression residuals indicated high spatial autocorrelation, which can lead to incorrect inferences by inflating degrees of freedom (Dormann et al. 2007). To address spatial autocorrelation in the models, the authors implemented spatial eigenvector map- ping (SEVM), which has been shown to account for spatial autocorrelation in regression models (Dormann et al. 2007; Diniz-Filho et al. 2008). For each census region, spatial filters were devel- oped using SEVM based on Gabriel connectivity matrices (following Diniz-Filho et al. 2008). These spatial filters describe the spatial arrange- ment of communities from the broadest pat- terns to increasingly finer-scaled patterns. Once extracted, the spatial filters can be included in the regression model as independent vari- ©2016 International Society of Arboriculture
March 2016
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