newdata argument in prediction function for natural spline and smoothing spline

Question

I am trying to plot a fitted spline with both ns() and smooth.spline() models. When I fit the spline I am unsure how I can set the newdata argument in the prediction function.

For the ns() model, it seems that I have to write the prediction function as predict(fit, newdata= list(x= x.grid)) such that I can plot the fitted curve. If I leave out the newdata argument it will pop the error of x y differing in length.

For the smooth.spline() model, the prediction looks like this predict(fit, x.grid)$y. If I add the newdata= argument it then returns me the x y differing in length error. Can someone explain why there is such a difference in the use of prediction function?

The code I am working on for natural spline model:

nob = 2
ncubic_ult = glm(mpg~ns(weight, df=2), data = Auto)
autote= Auto[te,]

testweightRange= range(autote$weight)
testweightgrid = seq( from=testweightRange[1], to=testweightRange[2], length.out=100 )
# prediction with list():
fittedmpg= predict(ncubic_ult, newdata = list(weight= testweightgrid))
plot( autote$weight, autote$mpg ,col='grey', main = 'newdata= list')
lines(testweightgrid, fittedmpg, col='red', lw=4)

Smoothing spline:

nob = 3
smooth_ult = smooth.spline(horsepower, mpg, df= nob)
autote= Auto[te,]
test_hpwRange= range(autote$horsepower)
test_hpwgrid = seq( from=test_hpwRange[1], to=test_hpwRange[2], length.out=100 )
fittedmpg= predict(smooth_ult,test_hpwgrid)$y
plot( autote$horsepower, autote$mpg ,col='grey', main = 'newdata= list')
lines(test_hpwgrid, fittedmpg, col='red', lw=4)

```

Answer 1

I don't know what te is, I have set it to 1:10.

In the first case using glm the function predict.glm needs a data frame with a column named like the predictor variable.

In the second case the return of predict.smooth.spline is a list with x as input data (vector) and y as fitted values (also a vector)..meaning a list of vectors.

Here is my working example for you:

library(splines)
library(ISLR) # for Auto datset: 

nob <- 2
ncubic_ult <- glm(mpg~ns(weight, df=2), data = Auto)

# don't now that te is... I set it to 1 to 10!
te <- 1:10
autote <- Auto[te,]

testweightRange <- range(autote$weight)
testweightgrid <- seq( from=testweightRange[1], to=testweightRange[2], length.out=100 )

# newdata; see ?predict.glm... it should be a data frame which to look for variables with which to predict!
new_data <- data.frame(weight = testweightgrid)

# prediction with newdata:
fittedmpg <- predict(ncubic_ult, newdata = new_data)
plot( autote$weight, autote$mpg ,col='grey', main = 'newdata= data.frame')
lines(testweightgrid, fittedmpg, col='red', lw=4)

nob <- 3
smooth_ult <- smooth.spline(Auto$horsepower, Auto$mpg, df= nob)
autote <- Auto[te,]
test_hpwRange <- range(autote$horsepower)
test_hpwgrid <- seq( from=test_hpwRange[1], to=test_hpwRange[2], length.out=100 )

# see ?predict.smooth.spline. the output is a list with x as input data and y fitted values. 

fittedmpg <- predict(smooth_ult, x = test_hpwgrid)
plot( autote$horsepower, autote$mpg ,col='grey', main = 'newdata= vector')
lines(test_hpwgrid, fittedmpg$y, col='red', lw=4)

^{Created on 2020-07-10 by the reprex package (v0.3.0)}