Dealing with missing data under stratified sampling designs where strata are study domains

TL;DR

This paper proposes Bayesian and frequentist methods to accurately estimate election results from stratified samples with missing data, especially when strata are also study domains, demonstrated through a Mexican quick count case study.

Contribution

It introduces novel Bayesian and frequentist approaches for partial estimation under stratified sampling with missing data, incorporating variance correction and dynamic post-stratification.

Findings

Both methods effectively estimate election composition with partial data.

The Bayesian approach improves variance estimation with credibility level correction.

The frequentist method adapts multiple imputation to stratified sampling with missing information.

Abstract

A quick count seeks to estimate the voting trends of an election and communicate them to the population on the evening of the same day of the election. In quick counts, the sampling is based on a stratified design of polling stations. Voting information is gathered gradually, often with no guarantee of obtaining the complete sample or even information in all the strata. However, accurate interval estimates with partial information must be obtained. Furthermore, this becomes more challenging if the strata are additionally study domains. To produce partial estimates, two strategies are proposed: 1) A Bayesian model using a dynamic post-stratification strategy and a single imputation process defined after a thorough analysis of historic voting information. Additionally, a credibility level correction is included to solve the underestimation of the variance; 2) a frequentist alternative that combines standard multiple imputation ideas with classic sampling techniques to obtain estimates under a missing information framework. Both solutions are illustrated and compared using information from the 2021 quick count. The aim was to estimate the composition of the Chamber of Deputies in Mexico.