## 2 Materials and Methods
### Methodology  
We first conducted Chi-square tests to assess the relationships between the evaluations of the living environments of both the current residences and hometowns, as well as the motivations for remaining in the current residence and for U-turn migration. We examined the differences in the influence of the living environments on each type of motivation to assess the influence of the current residence on U-turn motivation. Thereafter, we performed a decision tree analysis by using the Classification and Regression Tree (CART) method to assess the U-turn motivations according to respondents' evaluations of the living environments in their current residences and their hometowns. This time, we also focused on the gaps between the evaluations of the living environments in the current residences those of the hometowns. The decision tree analysis method was originally developed by [PERSON] et al. [41]. This method is known as the classification/regression tree analysis and is one of the machine learning methods for constructing prediction models from data [42]. The method involves generating a classifying model with hierarchical conditional branches. Samples for analysis can include both categorical and continuous variables, and one of the categorical variables is often used as a response while others are used as predictors. Based on these predictors, for each sample, which class it should be categorized in is systematically predicted. Decision tree analysis attracts considerable attention these days for the following two advantages: (1) clear visualization of conditional branch rules, (2) no need to standardize or perform other kinds of processes. Recently, due to its convenience and powerful algorithm, decision tree analysis has been applied in various research fields [43; 44; 45; 46]. The explanatory variables were separated into four categories:  
1. Evaluation of the living environments in the place of current residence (20 variables),
2. Evaluation of each living environment in the hometown (20 variables),
3. Differences in evaluations between both regions (20 variables), and
4. Traveling time between the region of current residence and hometown (1 variable). Each explanatory variable was treated on an interval scale. For categories 1 and 2, we used the 5-point evaluation of each living environment. These indices were to test the hypothesis that \"there may be some decisive living environments in each region.\" We assumed that if the evaluations of specific variables related to the current residence or hometown is above or below a certain value, then this living environment directly affects a person's propensity for U-turn migration, thus making it unnecessary to compare the gap. Indices in category 3 were calculated as the difference between an individual's evaluation of each living environment--of the current residence and hometown. These indices were integers ranging from \(-4\) to \(4\). A positive value indicates that the respondent favors the current place of residence over their hometown. A value of \(0\) suggests that the evaluations of both areas are almost equivalent. These indices were used to assess the hypothesis that \"people's motivation toward U-turn migration was sometimes decided by a comparison between the living environments in current residences and the hometowns.\" For the traveling time between the two regions, we used the route search service provided by Yahoo! Japan ([[https://transit.yahoo.co.jp/](https://transit.yahoo.co.jp/)]([https://transit.yahoo.co.jp/](https://transit.yahoo.co.jp/))) to determine the time required to travel between the public offices of both regions (no limitation for transportation methods). We calculated the values of the variance inflation factors for each of the sixty-one variables. None exceeded \(10\) and, therefore, we used all variables in the decision tree analysis. The CART method was used for selecting the variables for the model. The minimum sample size of a parent node was set at \(20\), and that of a child node at \(7\).