Prior Choice for the Variance Parameter in the Multilevel Regression and Poststratification Approach for Highly Selective Data. A Monte Carlo Simulation Study.

Abstract

The multilevel and poststratification approach is commonly used to draw valid inference from (non-probabilistic) surveys. This Bayesian approach includes varying regression coefficients for which prior distributions of their variance parameter must be specified. The choice of the distribution is far from being trivial and many contradicting recommendations exist in the literature. The prior choice may be even more challenging when data results from a highly selective inclusion mechanism, such as applied by volunteer panels. We conduct a Monte Carlo simulation study to evaluate the effect of different distribution choices on bias in the estimation of a proportion based on a sample that is subject to a highly selective inclusion mechanism.

Investigation of half-normal model using informative priors under Bayesian structure

“…Some recent important works related to simulation, the choice of complex priors related to HND, are done by various authors including Van Erp and Brown (2020) and Al Amer et al (2021), Sindhu and Hussain (2022), Ariyo et al (2022), Bruch and Felderer (2022), Martin et al (2022), among others. Here, we would like to summarize their work for the ready reference of the readers.…”

“…The results show that marginals perform far better over the conditional and the superiority of joint and separation priors over IW in all settings with selection criteria on a practical data set. Second is the work of Bruch and Felderer (2022), who considered prior choice for the variance parameter in multilevel regression and poststratification selective data and their Monte Carlo simulation study was done on the similar way as that of ours. They observed that prior choices are challenging when data results from selective inclusion mechanism which may be subject to bias in the estimation of a proportion based on a sample that is subject to a highly selective inclusion mechanism.…”