Contents
How do you fit a generalized additive model?
Let’s now fit an actual generalized additive model using the same cubic spline as our basis. We again use the gam function as before for basic model fitting, but now we are using a function s within the formula to denote the smooth terms.
What is the intercept of a generalized additive model?
The first plot represents the intercept of 470.44, the second plot, our \\ (b_2\\) coefficient of 289.5 multiplied by Income and so forth. The bottom plot shows the final fit \\ (f (x)\\), i.e. the linear combination of the basis functions.
How to fit generalized additive models in ggplot2?
The above graph represents a cubic spline with 8 knots 12 between the first and third quartiles. The red line uses the GAM functionality within ggplot2’s geom_smooth as a point of comparison. Let’s now fit an actual generalized additive model using the same cubic spline as our basis.
How are thin plate splines fitted in GAM?
Like other smoothing splines, thin plate splines are fitted using a generalized additive model (GAM), denoted by the equation: where β0 is a constant, ƒ (X) denotes a flexible function of x (or the sum of these functions for more than one x), and λ is the error term.
Is the cubic spline the same as thin plate?
Use of a cubic spline for x, as above, results in quite a different shape for the fitted function compared to the default thin-plate spline for that part of the space where x values are sparse. However, both models have almost identical results in terms of deviance explained and pattern of residuals.
How are Gams different from generalised linear models?
A GAM is a linear model with a key difference when compared to Generalised Linear Models such as Linear Regression. A GAM is allowed to learn non-linear features. GAMs relax the restriction that the relationship must be a simple weighted sum, and instead assume that the outcome can be modelled by a sum of arbitrary functions of each feature.