fertilization, and pesticide application. Consistent with best practices in multi-level modeling we first specified a three-level null model for each of the three dependent variables. The null model parses the variation in each household-level dependent variable across the higher-level neighborhood, and metropolitan regional scales. If the null model indicates that the responses appear to cluster by scale, then a more comprehensive model needed (56). Measures of household-level independent variables were subtracted from their grand means to improve interpretation (56). This approach first tests if a multi-level model is warranted or not. The null model is: (eq. 1) where is the response from household in Census block group in metropolitan π i j and is the household-level intercept in level-two (block group) in level-three k, j (metropolitan region) Because the response variables are binary, the log odds of were k. modeled instead. In Equation 1, ), ), ). No slopes are v00k ~ N(0, u0jk ~ N(0, eijk ~ N(0, specified in equation 1. is decomposed and estimated as a hierarchically nested set of regression equations: at Level 2 (Census block group): (eq. 2) at Level 3 (metropolitan region): (eq. 3) where represents a neighborhood-scale random effect, is a metropolitan regional-scale random effect, and is the household-scale residual error term. Here random means eijk
fertilization, and pesticide application. Consistent with best practices in multi-level modeling we first specified a three-level null model for each of the three dependent variables. The null model parses the variation in each household-level dependent variable across the higher-level neighborhood, and metropolitan regional scales. If the null model indicates that the responses appear to cluster by scale, then a more comprehensive model needed (56). Measures of household-level independent variables were subtracted from their grand means to improve interpretation (56). This approach first tests if a multi-level model is warranted or not. The null model is: (eq. 1) where π is the response from household i in Census block group j in metropolitan k, and is the household-level intercept in level-two (block group) j in level-three (metropolitan region) k. Because the response variables are binary, the log odds of were modeled instead. In Equation 1, v00k ~ N(0, ), u0jk ~ N(0, ), eijk ~ N(0, ). No slopes are specified in equation 1. is decomposed and estimated as a hierarchically nested set of regression equations: at Level 2 (Census block group): (eq. 2) at Level 3 (metropolitan region): (eq. 3) where represents a neighborhood-scale random effect, is a metropolitan regional-scale random effect, and eijk is the household-scale residual error term. Here random means
DHLockeDissertation_OfRecord.docx