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

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 and (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.

KEYWORDS:

• Clustering
• finite population sampling
• missing data
• multiple imputation
• quick count
• post-stratification

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62D05
• 62D10
• 62F15
• 62F40
• 62P25

Acknowledgements

The authors are grateful to the Electoral Federal Registry of the Electoral National Institute for the ongoing support in organizing the quick count. In particular to Arturo González Morales, former director of Statistics.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The nominal list is the register of citizens entitled to vote.

2 Geographically Mexico is divided into 300 federal districts. These districts are delimited to distribute the population of the country in a balanced manner so that each elected deputation represents a similar number of inhabitants.

3 Independent candidates, null plus unregistered votes and abstentions are not considered for proportional representation.