Arboriculture & Urban Forestry 40(2): March 2014 73 Table 1. Comparison of selected block-group demographics for study sample and City of Portland (SD = Standard Deviation). Currency is listed in U.S. dollars. Variable Percent owner occupied Percent non-Hispanic white Percent over 25 without high-school diploma Percent households making less than $50K Sample mean (SD) 64 (19) 79 (15) 9 (8) 49 (17) one sample point to the demographic characteris- tics of the whole city (410 block groups). For this comparison, 33 block groups were excluded because they were either primarily industrial or commercial (less than 50 households) or more than 50 percent of a block group fell outside the Portland city lim- its (Table 1). There were no statistically significant demographic differences between the sample and the whole city. This was true of all demographic variables, not just those presented in Table 1. STATISTICAL ANALYSIS In classical regression, it is assumed that observa- tions are independent. Unfortunately, the current data violates this assumption. Specifically, observa- tions in the same census block group are more alike than observations in different block groups. In addi- tion, the dependent variable is binary: 1 if a resident agreed to participate in a tree-planting program and 0 otherwise. Binary response data with intra block-group dependence can be accommodated us- ing a fixed-effects or a random-effects logit model: [1] Yi,j = α + βXi,j jth census block (1 if a respondent agreed to par- ticipate in the tree-planting program and 0 other- wise), Xi,j where Yi,j the block-group specific residual or intercept, and α and β are coefficients to be estimated in the regres- sion step. This model structure allows researchers to include independent variables that vary at the parcel level (e.g., number of street trees) and at the block- group level (e.g., high-school graduation rate). A fixed-effects model adds a block-group spe- is a vector of independent variables, vi cific intercept, whereas a random-effects model adds a block-group specific residual (one is a model parameter, whereas the other is a ran- dom variable). The intercept or residual serves the same purpose: if accounts for block-specific effects that are not explained by the independent + vi denotes the ith survey response in the is City mean (SD) 63 (20) 80 (14) 10 (9) 49 (18) variables. For example, respondents in a particu- lar block group may be more likely to participate in a tree-planting program, because traffic noise is a problem in that block group. The intercept or residual would account for this difference. A Hausman specification test was used to choose between a fixed-effects and a random-effects model. The null hypothesis of the Hausman test assumes that there is no systematic difference between model coefficients estimated using fixed-effects versus ran- dom-effects estimators (Greene 2000). If the null hypothesis holds, both estimators are consistent, but only the random-effects estimator is efficient. If the null hypothesis is rejected, the random-effects estimator is inconsistent. In the case of the current, the P-value for the Hausman test was 0.0546, and so the study authors narrowly failed to reject the null hypothesis using the customary P-value threshold of 0.05, and, therefore, use the random-effects esti- mator for the following analysis. Given the closeness of rejecting the null hypothesis, it is possible that the coefficient estimates are inconsistent. However, one can draw comfort from the fact that both the random- and fixed-effects estimators are unbiased. Variables were selected for inclusion in the final model using iterative backwards selection. Analysis began with the inclusion of a complete list of can- didate variables, although a variance-covariance matrix was used to avoid including highly collin- ear combinations of variables in the same model. For example, percent of residents with a college degree and percent without a high-school diploma have a correlation coefficient of -0.66, and so were not included in the same model. All variables with a p-value of greater than 0.8 were then dropped. This process was repeated with progressively lower P-value thresholds of 0.6, 0.4, 0.2, and 0.1. The only exception to this selection criterion was groups of dummy variables (e.g., canvasser dummy variables). If one dummy variable from a group was signifi- cant, then the entire group was retained. Because highly correlated combinations of variables in ©2014 International Society of Arboriculture
March 2014
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