Flexible modelling using basis expansions (Chapter 5) Linear ...

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The function stepAIC does all this for you:> ns.hr.step #> # Here we are at Table 5.1; note that alcohol has been dropped from the> # model2005-02-08Example: heart dataThe degrees of freedom fitted are the number of columns in the<strong>basis</strong> matrix (+ 1 for the intercept). This can also be computed as thetrace of the hat matrix, which can be extracted from lm. There issomething analogous for glm, because glm’s are fitted <strong>using</strong>iteratively reweighted least squares.
Smoothing splines◮ This is an approach closer to ridge regression. Put knots ateach distinct x value, and then shrink the coefficients bypenalizing the fit . (Figure 5.6)◮subject to:argmin βΣ i(yi − Σ j β j h j (x i ) ) 2β T Ωβ < c◮ with no constraint we get usual least squares◮ Ω controls the smoothness of the final fit:∫Ω jk = h j ′′ (x)h′′ k (x)dx◮ This solves the variational problemargmin fΣ i (y i − f (x i )) 2 + λ∫ ba{f ′′ (t)} 2 dt◮ the solution is a natural cubic spline with knots at each x i
Page 1 and 2: STA 450/4000 S: February 2 2005Flex
Page 4 and 5: Regression splines◮ Constraints o
Page 6 and 7: Regression splines◮ The B-spline
Page 8 and 9: Example: heart dataThe individual c
Page 12 and 13: Smoothing splines◮ How many param
Page 14: Smoothing splinesA smoothing spline

Flexible modelling using basis expansions (Chapter 5) Linear ...

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