Comparison of regression methods for phenology.

Several methods exist for investigation of the relationship between records and weather data. These can be broadly classified into models that attempt to incorporate information about underlying biological processes, such as those based on the concept of thermal time, and linear regression methods. The latter are less driven by the biology but have the advantages of ease of use and flexibility. Regression can be used where there is no obvious mechanistic model or to suggest the form of a mechanistic or empirical model where there are several to choose from. Stepwise regression is commonly used in phenology. However, it requires aggregation of the weather records, resulting in loss of information. Penalised signal regression (PSR) was recently introduced to overcome this weakness. Here, we introduce a further method to the phenology context called fusion, which is a sparse version of PSR. In this paper, we compare the performance of these three regression methods based on simulations from two types of mechanistic models, the spring warming and sequential models. Given a suitable choice of temperature days as regression covariates, PSR and fusion performed better than stepwise regression for the spring warming model and PSR performed best for the sequential model. However, if a large number of redundant temperature days were included as covariates, the performance of PSR fell off whilst fusion was quite robust to this change. For this reason, it is best to use PSR and fusion methods in tandem, and to vary the number of covariates included.