#StackBounty: #r #model #fitting #splines #derivative How can I fit a spline to data that contains values and 1st/2nd derivitives?

Bounty: 50

I have a dataset that contains let’s say some mesurements for position, speed and acciliration. All come from the same “run”. I could construct a linear system and fit a polynome to all of those measurements.

But can I do the same with splines? What is an ‘R’ way of doing this?

Here is some simulated data I would like to fit:

f <- function(x) 2+x-0.5*x^2+rnorm(length(x), mean=0, sd=0.1)
df <- function(x) 1-x+rnorm(length(x), mean=0, sd=0.3)
ddf <- function(x) -1+rnorm(length(x), mean=0, sd=0.6)

x_f <- runif(5, 0, 5)
x_df <- runif(8, 3, 8)
x_ddf <- runif(10, 4, 9)

data <- data.frame(type=rep('f'), x=x_f, y=f(x_f))
data <- rbind(data, data.frame(type=rep('df'), x=x_df, y=df(x_df)))
data <- rbind(data, data.frame(type=rep('ddf'), x=x_ddf, y=ddf(x_ddf)))

ggplot(data, aes(x, y, color=type)) + geom_point()

m <- lm(data$y ~ bs(data$x, degree=6)) # but I want to fit on f, df, ddf. possible?

enter image description here

Get this bounty!!!

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