Practice MGCV
Basics of gam model
- When the relationship is almost linear \(df = 1\), the confidence interval are zero when the estimates is zero due to the identifiability constrain. This restriction sets the mean value of \(f\) to zero, such as there is no uncertainty when \(f = 0\).
- The points on the smoothed effects are just the partial residual, which simple are the Pearson residuals plus the smooth function for the corresponding covariate being plotted.
- Considering an initial model with \(k_1\) knots and \(df<k_1 -1\); then, increasing the number of knot to \(k_2\), can modified the number of effective degrees of freedom. It happens because different subspace of functions are obtained when \(k=k_1\) or \(k+k_2\) for a particular \(df\).
- Smoother functions can be obtained introducing and additional parameter to the GCV score \(\gamma\). For example, \(\gamma = 1.4\) is suggested to avoid overfitting without compromising model fit.
Smoothing several variables
- We can use thin plate regression spline or tensor products.