Gerrymandering is the act of manipulating the boundaries of an electoral district so as to favor one party or group. There have been some attempts to explicitly quantify how much a district "meanders" or twists. By a mathematical structure called the medial axis which is essentially the skeleton of a given shape, we introduce a new measure to deal with quantification of district meandering. We performed analysis on the 18 districts in the state of Pennsylvania in the year 2015 as well as in the year 2018, after the district boundaries were redrawn in an attempt to reduce gerrymandering. By comparing our results with previous research in the field, we found that our proposed measure gives more reasonable and stable results and addresses some issues from the previous research such as partial gerrymandering and bias against larger districts.
“ … -by-Step Guide Using JMP. Cary, NC:SAS Institute Inc. Zhong,Mushan and Roger Hoerl. “Use of Nonlinear Models in Analyzing Experiments with … and Vining 2000) Mushan Zhong (2019) looked at other nonlinear models that … ”
Abstract
Mixture variables are unique as the components must sum to 1, causing problems when there is interaction between mixture and process variables. The best model is the fully linearized model, but this can get large quickly. We began by comparing models on multiple data sets. These models include linear and nonlinear models. After seeing that nonlinear models appear to be the best alternatives, we used the systematically selected fractions of each data set in order to obtain an in and out of sample RMSE. This allows us to see if there is evidence of overfitting, how well the model predicts out of sample, and how well the model fits the training data. To increase the number of data points, we used bootstrapping to create a random sample that is proportional to the size of the full data set. The resulting RMSEs indicated that Zhong's model and the fully linearized model had extreme evidence of overfitting. Thus, we considered the other 3 models as better options. There was evidence of overfitting for these models with two data sets. The models seemed to do better for the Prescott data, which is interesting as it is the largest data set and the only data set where the mixture variables have constraints and the process variables have 3 levels. Within the Prescott data sets, the SHB nonlinear appears to perform the best with the least evidence of overfitting, so we conclude that this is in general the best alternative to the fully linearized model.
