Using Random Effects to Build Impact Models When the Available Historical Record Is Short

Filipe Aires Estellus, S.A.S., Paris, France

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Abstract

The analysis of the affect of weather and climate on human activities requires the construction of impact models that are able to describe the complex links between weather and socioeconomic data. In practice, one of the biggest challenges is the lack of data, because it is generally difficult to obtain time series that are long enough. As a consequence, derived impact models predict well the historical record but are unable to perform well on real forecasts. To avoid this data-limitation problem, it is possible to train the impact model over a large spatial domain by “pooling” data from multiple locations. This general impact model needs to be spatially corrected to take local conditions into account, however. This is particularly true, for example, in agriculture: it is not efficient to pool all of the spatial data into a single very general impact model, but it is also not efficient to develop one impact model for each spatial location. To solve these aggregation problems, mixed-effects (ME) models have been developed. They are based on the idea that each datum belongs to a particular group, and the ME model takes into account the particularities of each group. In this paper, ME models and, in particular, random-effects (RE) models are tested and are compared with more-traditional methods using a real-world application: the sales of salt for winter road deicing by public service vehicles. It is shown that the performance of RE models is higher than that of more-traditional regression models. The development of impact models should strongly benefit from the use of RE and ME models.

Additional affiliation: Laboratoire de l’Etude du Rayonnement et de la Matière en Astrophysique, Centre National de la Recherche Scientifique/Observatoire de Paris, Paris, France.

Corresponding author address: F. Aires, Estellus, LERMA, Observatoire de Paris, 61, Ave. de l’Observatoire, 74014 Paris, France. E-mail: filipe.aires@estellus.fr

Abstract

The analysis of the affect of weather and climate on human activities requires the construction of impact models that are able to describe the complex links between weather and socioeconomic data. In practice, one of the biggest challenges is the lack of data, because it is generally difficult to obtain time series that are long enough. As a consequence, derived impact models predict well the historical record but are unable to perform well on real forecasts. To avoid this data-limitation problem, it is possible to train the impact model over a large spatial domain by “pooling” data from multiple locations. This general impact model needs to be spatially corrected to take local conditions into account, however. This is particularly true, for example, in agriculture: it is not efficient to pool all of the spatial data into a single very general impact model, but it is also not efficient to develop one impact model for each spatial location. To solve these aggregation problems, mixed-effects (ME) models have been developed. They are based on the idea that each datum belongs to a particular group, and the ME model takes into account the particularities of each group. In this paper, ME models and, in particular, random-effects (RE) models are tested and are compared with more-traditional methods using a real-world application: the sales of salt for winter road deicing by public service vehicles. It is shown that the performance of RE models is higher than that of more-traditional regression models. The development of impact models should strongly benefit from the use of RE and ME models.

Additional affiliation: Laboratoire de l’Etude du Rayonnement et de la Matière en Astrophysique, Centre National de la Recherche Scientifique/Observatoire de Paris, Paris, France.

Corresponding author address: F. Aires, Estellus, LERMA, Observatoire de Paris, 61, Ave. de l’Observatoire, 74014 Paris, France. E-mail: filipe.aires@estellus.fr
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