Search code examples
rsplinebsplinecubic-spline

Monotone spline in R

I'm trying to use the spline2 package in R to build a monotone spline.

I'm having trouble in evaluating the model for new values of the independent variable. In general, I'm having trouble grasping R treatment of "predict" and its relation to spline2, and how to use the bs object produced.

I tried to follow this example which uses spline1. My data is in a dataframe named BRIyII, with independent variable t and dependent variable P so: 

plot(BRIyII$t,BRIyII$P)

yields: enter image description here

So I do: 

knots=c(9)
myMat=mSpline(BRIyII$t, knots = knots, degree = 3, intercept = TRUE)
mylm=lm(BRIyII$P~myMat)

Now, if we:

pr = predict(mylm,data.frame(BRIyII$t))
points(BRIyII$t,pr,col = "red")

It yields: enter image description here

So my questions are:

1- Since the rightmost predicted value (red dot) is lower than the one to its left, am I misunderstanding the "monotonic" nature of the m splines ?

2- How can I evaluate the spline in values other than those defined in BRIyII$t ? I tried several combinations of stuff but I lack the R syntax knowledge. I would ideally want to do something like : 

newdata=seq.int(0,41.5,0.1)
Solution

  • I'll address Question #1 because Question #2 is addressed in the comments.

    The splines2 documentation refers to M-spline basis as the "monotone regression spline" basis, but I think this is misleading. The way to estimate a monotone regression spline is to use the I-spline basis, with the restriction that the regression coefficients be non-negative. I-splines are the integrals of M-splines and are thus non-decreasing. So any non-negative linear combination of them will also be non-decreasing. So you can use the splines2::iSpline along with a non-negative regression method like nnls::nnls to estimate a monotone regression function.

    For an explanation of M-splines, I-splines and monotone regression, check out:

    Ramsay, JO (1988) Monotone regression splines in action. Statistical Science 3(4), 425-461.