# spline : difference between smooth.spline() & bSpline() ?

Hi,

Can someone explain me three questions related to smooth.spline().
1°) Why the knots created within smooth.spline are no evenly spread?
2°) What type of spline is used by smooth.spline ?
When I compare a smooth.spline with no constraint (spar=0) and compare it with a linear model using a B-spline (bSpline function) I have very close curves but identical and the parameters differs.
3°) How can I retrieve the spline matrix from smooth.spline as the one I have from bSpline?

Here is the code I have used :
y18 <- c(1:3, 5, 4, 7:3, 2*(2:5), rep(10, 4))
data <- data.frame(y18, x=seq(0,1,length=18))

xx <- seq(0, 1, len = 201)
s2 <- smooth.spline(y=data\$y18, x=data\$x, nknots = 9, spar=0 )
p <- predict(s2, xx)

# bsx <- data.frame(bSpline(x=data\$x , knots=1:7/8, degree = 3)) #--- 7 internes + 2 externes => 9 noeuds

bsx <- data.frame(bSpline(x=data\$x , knots=s2\$fit\$knot[5:11], degree=3, intercept = FALSE))
data <- data.frame(data, bsx)

bs100 <- data.frame(bSpline(x=0:100/100, knots=s2\$fit\$knot[5:11], degree=3, intercept = FALSE))
bs100 <- data.frame(x=0:100/100, bs100)

lm_y18 <- lm(data=data[,-2], y18 ~ .)
bs100\$y <- predict(lm_y18, bs100)

#---- question 1 ----
s2\$fit\$knot
diff(s2\$fit\$knot)

#---- question 2 ----
ggplot() + geom_point(data=data, aes(x=x, y=y18)) +
geom_line(aes(x=p\$x, y=p\$y)) +
geom_line(aes(x=p02\$x, y=p02\$y)) +
geom_line(aes(x=bs100\$x, y=bs100\$y), color=2) +
scale_x_continuous(labels = scales::percent) +
geom_vline(xintercept=s2\$fit\$knot, lty=2, color="grey")
cbind(s2\$fit\$coef,lm_y18\$coefficients, s2\$fit\$coef-lm_y18\$coefficients)

s02 <- smooth.spline(y=data\$y18, x=data\$x, nknots = 9, spar=0.2 )
p02 <- predict(s02, xx)

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