MGCV get design matrix

Question

GAM regression with splines basis is defined by the following cost function:

cost = ||y - S \beta ||^2 + scale * integral(|S'' \beta|^2)

where S is the design matrix defined by the splines.

In R I can compute gam with the following code:

library('mgcv')
data = data.frame('x'=c(1,2,3,4,5), 'y'=c(1,0,0,0,1))

g = gam(y~s(x, k = 4),family = 'binomial', data = data, scale = 0.5)
plot(g)

I would like to get the design matrix S that is generated by s() function.

How can I do that?

Answer 1

I believe there are two ways to get the design matrix from a gamObject

library('mgcv')
data <- data.frame('x'=c(1,2,3,4,5), 'y'=c(1,0,0,0,1))

g <-  gam(y~s(x, k = 4),family = 'binomial', data = data, scale = 0.5)
plot(g)

(option1 <- predict(g, type = "lpmatrix"))
# (Intercept)      s(x).1      s(x).2     s(x).3
# 1           1  1.18270529 -0.39063809 -1.4142136
# 2           1  0.94027407  0.07402655 -0.7071068
# 3           1 -0.03736554  0.32947477  0.0000000
# 4           1 -0.97272283  0.21209396  0.7071068
# 5           1 -1.11289099 -0.22495720  1.4142136
# attr(,"model.offset")
# [1] 0
(option2 <- model.matrix.gam(g))
# (Intercept)      s(x).1      s(x).2     s(x).3
# 1           1  1.18270529 -0.39063809 -1.4142136
# 2           1  0.94027407  0.07402655 -0.7071068
# 3           1 -0.03736554  0.32947477  0.0000000
# 4           1 -0.97272283  0.21209396  0.7071068
# 5           1 -1.11289099 -0.22495720  1.4142136
# attr(,"model.offset")
# [1] 0