A multilevel Bayesian framework for predicting municipal waste generation rates

Prediction of waste production is an essential part of the design and planning of waste management systems. The quality and applicability of such predictions depend heavily on model assumptions and the structure of the collected data. Ordinarily, municipal waste generation data are organized in hierarchical structures with municipal or county levels, and multilevel models can be used to generalize linear regression by directly incorporating the structure into the model. However, small amounts of data can limit the applicability of multilevel models and provide biased estimates. To cope with this problem, Bayesian estimation is often recommended as an alternative to frequentist estimation, such as least squares or maximum likelihood estimation. This paper proposes a multilevel framework under a Bayesian approach to model municipal waste generation with hierarchical data structures. Using a real-world dataset of municipal waste generation in Denmark, the predictive accuracy of multilevel models is compared to aggregated and disaggregated Bayesian models using socio-economic external variables. Results show that Bayesian multilevel models outperform the other models in prediction accuracy, based on the leave-one-out information criterion. A comparison of the Bayesian approach with its frequentist alternative shows that the Bayesian model is more conservative in coefficient estimation, with estimates shrinking to the grand mean and broader credible intervals, in contrast with narrower confidence intervals produced by the frequentist models.