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Income, education, and other poverty-related variables: a journey through Bayesian hierarchical models

Irving Gómez-Méndez, Chainarong Amornbunchornvej

Abstract

One-shirt-size policy cannot handle poverty issues well since each area has its unique challenges, while having a custom-made policy for each area separately is unrealistic due to limitation of resources as well as having issues of ignoring dependencies of characteristics between different areas. In this work, we propose to use Bayesian hierarchical models which can potentially explain the data regarding income and other poverty-related variables in the multi-resolution governing structural data of Thailand. We discuss the journey of how we design each model from simple to more complex ones, estimate their performance in terms of variable explanation and complexity, discuss models' drawbacks, as well as propose the solutions to fix issues in the lens of Bayesian hierarchical models in order to get insight from data. We found that Bayesian hierarchical models performed better than both complete pooling (single policy) and no pooling models (custom-made policy). Additionally, by adding the year-of-education variable, the hierarchical model enriches its performance of variable explanation. We found that having a higher education level increases significantly the households' income for all the regions in Thailand. The impact of the region in the households' income is almost vanished when education level or years of education are considered. Therefore, education might have a mediation role between regions and the income. Our work can serve as a guideline for other countries that require the Bayesian hierarchical approach to model their variables and get insight from data.

Income, education, and other poverty-related variables: a journey through Bayesian hierarchical models

Abstract

One-shirt-size policy cannot handle poverty issues well since each area has its unique challenges, while having a custom-made policy for each area separately is unrealistic due to limitation of resources as well as having issues of ignoring dependencies of characteristics between different areas. In this work, we propose to use Bayesian hierarchical models which can potentially explain the data regarding income and other poverty-related variables in the multi-resolution governing structural data of Thailand. We discuss the journey of how we design each model from simple to more complex ones, estimate their performance in terms of variable explanation and complexity, discuss models' drawbacks, as well as propose the solutions to fix issues in the lens of Bayesian hierarchical models in order to get insight from data. We found that Bayesian hierarchical models performed better than both complete pooling (single policy) and no pooling models (custom-made policy). Additionally, by adding the year-of-education variable, the hierarchical model enriches its performance of variable explanation. We found that having a higher education level increases significantly the households' income for all the regions in Thailand. The impact of the region in the households' income is almost vanished when education level or years of education are considered. Therefore, education might have a mediation role between regions and the income. Our work can serve as a guideline for other countries that require the Bayesian hierarchical approach to model their variables and get insight from data.
Paper Structure (52 sections, 62 equations, 32 figures, 6 tables)

This paper contains 52 sections, 62 equations, 32 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related works
  3. Relevance of Bayesian hierarchical models
  4. Methodology
  5. Data and related information
  6. Comparison of models
  7. Variables to analyze
  8. Hierarchical model with one cluster: income per region
  9. No pooling model and complete pooling model
  10. No pooling model
  11. Complete pooling model
  12. Hierarchical model with common within-cluster variance
  13. Conditional posterior for $\theta_j$
  14. Conditional posterior for $\mu$
  15. Conditional posterior for $\sigma^2$
  16. ...and 37 more sections

Figures (32)

  • Figure 1: Boxplots of the 10 poverty-related variables affecting the largest percentage of households in Thailand.
  • Figure 2: Graphical representation of the considered models. Left: Separate independent models for each region, if we add the restrictions $\theta_j=\theta$ and $\sigma^2_j=\sigma^2$ for all $j$, then we get the complete pooling model. Center: Hierarchical model, where the regional means share a common structure, yet allowing them to be different, but the constraint of equal variance is still present. Right: Hierarchical model imposing a common structure for both, the regional means and the within-region variances.
  • Figure 3: Results considering independent separate models for each region. On the top row we show the regional mean, $\theta_j$ (left) and the regional standard deviation, $\sigma_j$ (right). On the bottom we show the province mean.
  • Figure 4: Results considering the complete pooling model for all the regions. On the top row we show the regional mean, $\theta_j$ (left) and the regional standard deviation, $\sigma_j$ (right). On the bottom we show the province mean.
  • Figure 5: Results considering a hierarchical model. We allow the mean of each region to vary while maintaining the same within-region variance $\sigma^2$. On the top row we show the regional mean, $\theta_j$ (left) and the regional standard deviation, $\sigma_j$ (right). On the bottom we show the province mean.
  • ...and 27 more figures