Modeling approaches to estimate community annoyance due to sonic booms using data from repeated surveys

In an on-going project for NASA, we are developing a modeling approach to analyze the relationship between the noise level of sonic booms from an experimental supersonic plane and the level of annoyance measured through community response surveys. The goal of the project is to obtain a quantitative relationship between noise level and annoyance that is representative for the affected population. Particular modeling challenges include multiple annoyance measurements per survey respondent and very few occurrences of annoyance overall. To address these challenges, we propose a two-stage model for the presence of high annoyance, with the first stage modeling the probability that a respondent is ever highly annoyed and the second stage a multilevel logistic regression model for high annoyance based on noise level and demographic characteristics. We use a variation of Multilevel Regression and Poststratification (Gelman and Little, 1997) to obtain an overall representative noise-annoyance curve for the population. The approach is applied to data from a NASA pilot study.