120 xi Zhang and Zheng: Assessments of Citizen Willingness to Support Urban Forestry represent the socio-economic characteristics, such as “family size,” “child < 18-years-old,” education level, race, gender, age, and income. The variable of “awareness of tree service” is defined as the total number of forestry agencies he/she knows, including the USDA Forest Service, the National Arbor Day Foundation, the International Society of Arboriculture, the Alabama Coopera- tive Extension System, the Alabama Forestry Commission, and the Auburn University School of Forestry and Wildlife Sciences. For specific preferences, such as choosing the presence of trees at their home and communities, as well as special financial channels to support urban forestry, the ordered logistic model is applied instead of ordinary linear regression. Following the work of Zavoina and McElvey (1975), as discussed by Greene (1993), the ordered logistic model is set up in the following manner: [3] yj = β’x + ε where yj is the level of choice to measure the preference to the dependent variables: “Having tree on property” (y1), “Having tree in community”(y2), and the support for “Alcohol & tobacco tax” (y3), respectively. The dependent variables are of three choices: low level of importance (scale = 6 or 7); median level of impor- tance (scale = 3 to 5); high level of importance (scale = 1 or 2). The value x is a vector of explanatory variables, β an unknown parameter vector, and ε is the error term. ε is assumed to have a standard logistic distribution with mean 0 and variance π2/3 . The marginal effects are nonlinear functions of the parameter estimates and levels of the explanatory variables. Hence, they generally cannot be inferred directly from parameter estimates. Marginal effects for distributions can be derived as follows: [4] Table 1. Statistical summary of the participants. Variables Should donate money Would donate money Annual income (in USD $1,000) Age Family size # of children < 18 years old Employee status Employed Retired and unemployed Education level ≤ high school Some college Bachelor’s or higher Race African-American or others White/Caucasian Male 14 85 60 tired. The education level is relatively high: 61% with a bachelor’s degree or higher. The respondents’ average household income is USD $66,280 which is relatively high compared to Alabama’s av- erage level of $42,000 in 2007. Approximately 85% of them are white and 13% are African-American; 60% of respondents are male. The results indicate that people like trees in general (Table 2). “Improve the appearance of the community” and “Improvement in air quality” are considered the most important benefits of trees by the largest percentage of people. Attitudes toward the negative impacts are quite mixed: the potential cause for property damage is the most concerning factor. More importantly, the magnitude of the beneficial responses is never above 3, yet all of the negative im- pacts are above 3, suggesting the public’s preference for the benefits of trees outweigh the negative sides or costs of maintaining trees. The results indicate 80%–90% of respondents strongly agree that tree ordinances should be required on public property and new construction sites, but only 30% strongly agree that tree ordi- nances should be applied to individual-owned yards. Apparently, households prefer more flexibility to manage their own property. In the survey, respondents were asked to indicate their atti- Based on the equation (4), researchers can see one variable’s marginal effect is related not only to its own coefficient, but also to the values of all other coefficients. Moreover, each observa- tion and each level carry a distinct set of marginal effect values. In practice, marginal effects are generally calculated using the parameter final point estimates and average variable values. In this study, the marginal effects are calculated separately for ev- ery observation at three levels, respectively. The results are then averaged to provide a single, average response estimate for ev- ery variable, recognizing cumulative effects across the region. Results obtained in this way anticipate more global changes for the population of points and respect the multivariate dis- tribution of parameter values (Wang and Kockelman 2009). RESULTS Table 1 lists the descriptive statistics of the study’s data. Half of the respondents are employed full-time and one-third of them are re- ©2011 International Society of Arboriculture tudes toward “having trees on property” and “having trees in a community.” The results show 85% of respondents who are look- ing for a residence such as a house or apartment indicate that having trees on the property is important, and more than 90% of respondents rate “having trees in the community” as important. One interesting question to ask is whether this preference is associated with socio-economic and demographic char- acteristics of the individuals. The ordered logistic model is applied in the investigation. Ordered logistic regression as- sumes the coefficients that describe the relationship between the lowest versus all higher categories of the response vari- able are the same as those that describe the relationship be- tween the next lowest category and all higher categories. This is called the proportional odds assumption (McCullagh 1980; Kim 2002). This assumption is rather strong and needs to be checked. The test result for the proportional odds assumption is not significant, suggesting that the assumption is satisfied and the ordered logistic regression is appropriate in this study. The regression results and the corresponding marginal effects are provided in Table 3. The χ2 value of 15.22 and 15.94 sug- Mean (std. dev) 48 (50) 34 (36) 66 (33) 51 (13) 2 (1) 0.49 (0.93) Frequency (%) N = 476 60 39 13 25 61
May 2011
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