R Tutorial: Basis functions and smoothing

Key Takeaways

now that you have a sense of how gams can fit nonlinear data let's learn a bit more about how they work gams are powerful because of their ability to take on many shapes but this is also it makes them challenging their flexibility makes it easy to over fit your data here we'll learn how smoothing helps us deal with this issue in general we want to balance two things when fitting a nonlinear model we want a model that captures the relationship by being close to the data but we also want to avoid fitting our model to noise or overfitting how well the GAM captures patterns and the data is measured by a term called likelihood its complexity or how much the curve changes shape is measured by wiggliness the key to a good fit is the trade-off between the two this trade-off is expressed by this simple equation with a smoothing parameter or a lambda value controlling the balance this smoothing parameter is optimized when R fits a gam to data here are plots of three gams with different smoothing or lambda values as you can see the one on the Left smoothes too much creating a straight line through curve data the one in the middle smoothes too little fitting noise ah rather than the trend the one on the right is just right its lambda value balances over and under fitting normally when we fit a model with mg Seavey's gam function we let the package do the work of selecting a smoothing parameter however we can fix the smoothing parameter to a value of our choosing via the SP argument the SP argument can be set for the whole model vien argument to the GAM function as in the first line of code we can also set the SP argument for a specific term in the GAM formula as shown in the second line of code instead if we allow our to do this work for us the mg CV package offers different methods for selecting smoothing parameters I and most gam experts strongly recommend that you fit models with their Remmel or restricted maximum likelihood method while different methods have their advantages Remmel is most likely to give you stable reliable results in addition to the smoothing parameter the other factor that affects how Wiggly a gam function can be is the number of basis functions that make up a smooth function here I've plotted gams with three seven and twelve basis functions all fit to the same data as you can see a smooth with a small number of basis functions is limited in its wiggliness while one with many basis functions is capable of capturing finer patterns to set the number of basis functions in a smooth we use the K argument in the smooth function in a gam formula setting this value to low will prevent the model from being sufficiently Wiggly if it's high though the automatic smoothing parameter selection will prevent it from being too Wiggly we just don't want to set it very high which can result in a model with more parameters than data or one that is slow to fit later in the model testing portion of the course we will learn how to test if the number of basis functions are adequate to fit our data now let's explore gams with different smoothing parameters and different numbers of basis functions