Identifying Linear Models in Multi-Resolution Population Data Using Minimum Description Length Principle to Predict Household Income

One shirt size cannot fit everybody, while we cannot make a unique shirt that fits perfectly for everyone because of resource limitations. This analogy is true for policy making as well. Policy makers cannot make a single policy to solve all problems for all regions because each region has its own unique issue. At the other extreme, policy makers also cannot make a policy for each small village due to resource limitations. Would it be better if we can find a set of largest regions such that the population of each region within this set has common issues and we can make a single policy for them? In this work, we propose a framework using regression analysis and Minimum Description Length (MDL) to find a set of largest areas that have common indicators, which can be used to predict household incomes efficiently. Given a set of household features, and a multi-resolution partition that represents administrative divisions, our framework reports a set C* of largest subdivisions that have a common predictive model for population-income prediction. We formalize the problem of finding C* and propose an algorithm that can find C* correctly. We use both simulation datasets as well as a real-world dataset of Thailand's population household information to demonstrate our framework performance and application. The results show that our framework performance is better than the baseline methods. Moreover, we demonstrate that the results of our method can be used to find indicators of income prediction for many areas in Thailand. By adjusting these indicator values via policies, we expect people in these areas to gain more incomes. Hence, the policy makers will be able to make policies by using these indicators in our results as a guideline to solve low-income issues. Our framework can be used to support policy makers in making policies regarding any other dependent variable beyond income in order to combat poverty and other issues. We provide the R package, MRReg, which is the implementation of our framework in the R language. The MRReg package comes with a documentation for anyone who is interested in analyzing linear regression on multi-resolution population data.