Inclusive Ranking of Indian States and Union Territories via Bayesian Bradley-Terry Model

Abstract

Ranking geographical or administrative units, such as countries or states, is a well-known approach for comparing developmental progress and informing evidence-based policymaking. Existing ranking methodologies typically rely on a single indicator, such as Gross Domestic Product (GDP), or a limited subset of indicators, e.g., the Human Development Index (HDI). However, to the best of our knowledge, a ranking methodology based on a large set of indicator variables is not available in the literature. To address this gap, we present an inclusive ranking methodology. We utilize the Bayesian Bradley-Terry (BT) model, which allows us to incorporate relevant prior information. We model the prior covariance of the BT merit parameters using an independent covariate, such that units with similar covariate values exhibit higher covariance, which decays as differences in the covariate increase. A hybrid of Metropolis-Hastings with preconditioned Crank-Nicolson proposal and Gibbs sampling scheme is used to estimate the merit parameters. The proposed methodology has been shown to converge, and a ranking-based stopping rule is proposed. We apply this methodology to rank the states and union territories (UTs) of India using data from the National Family Health Survey-5. We estimate and compare rankings under different regimes, e.g., all states/UTs, low-income states/UTs, mid-income states/UTs, and states/UTs by removing high-income states/UTs. Our results reveal meaningful deviations between economic standing and overall performance.