Estimating mixture models for environmental noise assessment

Environmental noise - linked to traffic, industrial activities, wind farms, etc. - is a matter of increasing concern as its association with sleep deprivation and a variety of health conditions has been studied in more detail. The framework used for noise assessments assumes that there is a basic level of background noise, which will often vary with time of day and spatially across monitoring locations, plus additional noise components from random sources such as vehicles, machinery or wind affecting trees. The question that has to be investigated is whether, and by how much, the noise at each location will be increased by the addition of one or more new sources of noise such as a road, a factory or a wind farm. The paper adopts a mixtures specification to identify heterogeneity in the sources and levels of background noise. In particular, it is important to distinguish between sources of background noise that may be associated with covariates of noise from a new source and other sources that are independent of these covariates. A further consideration is that noise levels are not additive, though sound pressures are. The analysis uses an extended version of Partha Deb’s Stata command (fmm) for estimating finite mixture models. The extended command allows for the imposition of restrictions such as that not all components are affected by the covariates or that the probabilities that particular components are observed depend upon exogenous factors. These extensions allow for a richer specification of the determinants of observed noise levels. The extended command is supplemented by post-estimation commands which use Monte Carlo methods to estimate how a new source will affect the noise exposure at different locations and how outcomes may be affected by noise control measures. The goal is to produce results that can be understood by decision-makers with little or no statistical background.