R: creating (non-B) splines?

Question

I want to replicate in R figures 5.1 and 5.2 of the Elements of Statistical learning (Hastie et al), . The authors show how to derive a cubic splines. These splines are not in the B-basis.

Can I use package splines to do this (I want to use it instead of manual coding, hoping the former will be more efficient) ? It seems bs() and ns() will only create b/natural splines. Is there a way to obtain simple splines? These would be (equation 5.3 in ESL):

• $h_1(x) = 1$, $h_2(x) = x$
• $h_3(x) = x^2$, * $h_4(x) = x^3$
• $h_5(x) = (x-\xi)^3_+$,

Thanks!

Answer 1

I do not know if you are still interested in this. You can obtain the spline functions you mention in your question with few lines of code

tpower = function(x, t, p) (x - t) ^ p * (x > t)

tpf_bases = function(x, knots, deg = 3)
{    
    X = matrix(0, nrow = length(x), ncol = deg)
    for(i in 1:deg) X[, i] = x^i
    X = cbind(1, X)

    Z = outer(x, knots, tpower, deg)
    Z = Z * (Z > 0)
    return(list(X = X, Z = Z))

}

x     = 1:10
bases = tpf_bases(x, deg = 3, knots = c(2, 3, 4))
X     = bases$X # x^0, x^1,...
Z     = bases$Z # Truncated power part

If you are interested also in the relationship between B-splines and truncated power bases, you could give a look to this discussion: Splines - basis functions - clarification

If you are also interested in how to fit penalized splines using the bases just defined, you can give a look here: Representing a GAM with truncated power basis as a mixed model

Hope this helps a bit and replies (at least partially) to the original question.