I am doing some modelling work in which I am trying to parametrise an effect that varies with season and time of day. The time of day effect differs between seasons in a complex way so it seems the most general approach is to model the effect in a periodic [time of day, day of year] space.
The effect being described has a non-linear relationship to the actual predictor and predicted quantities, so I need an explicit parametrisation that I can tune using non-linear optimisation.
So, the most obvious option would be a 2D Fourier basis. Can anyone recommend an R package for generating this? I found the package fda which has the function ‘create.fourier.basis’ but this appears to only apply to 1D.
Beyond a Fourier approach, the sampling of the data I have is highly irregular in the [time of day, day of year] plane so ideally a more localised approach such as a periodic cubic spline in which I can place more knots in the data rich parts of the plane would be preferable. Does anyone know of an R package that creates a 2D basis for this kind of representation?
The mgcv package can create tensor product basis functions of two or more underlying basis functions. It also allows for cyclic cubic and p splines, which can be used for the variables you mention, as the underlying basis functions for the tensor product.
As mgcv comes with R I would start with that. Look at
?teand?smooth.termsfor starters.