Question

Using the segmented package to create a piecewise linear regression I am seeing an error when I try to set my own breakpoints; it seems only when I try to set more than two.

(EDIT) Here is the code I am using:

# data
bullard <- structure(list(Rt = c(0, 4.0054, 25.1858, 27.9998, 35.7259, 39.0769, 
45.1805, 45.6717, 48.3419, 51.5661, 64.1578, 66.828, 111.1613, 
114.2518, 121.8681, 146.0591, 148.8134, 164.6219, 176.522, 177.9578, 
180.8773, 187.1846, 210.5131, 211.483, 230.2598, 262.3549, 266.2318, 
303.3181, 329.4067, 335.0262, 337.8323, 343.1142, 352.2322, 367.8386, 
380.09, 388.5412, 390.4162, 395.6409), Tem = c(15.248, 15.4523, 
16.0761, 16.2013, 16.5914, 16.8777, 17.3545, 17.3877, 17.5307, 
17.7079, 18.4177, 18.575, 19.8261, 19.9731, 20.4074, 21.2622, 
21.4117, 22.1776, 23.4835, 23.6738, 23.9973, 24.4976, 25.7585, 
26.0231, 28.5495, 30.8602, 31.3067, 37.3183, 39.2858, 39.4731, 
39.6756, 39.9271, 40.6634, 42.3641, 43.9158, 44.1891, 44.3563, 
44.5837)), .Names = c("Rt", "Tem"), class = "data.frame", row.names = c(NA, 
-38L))

library(segmented)

# create a linear model
out.lm <- lm(Tem ~ Rt, data=bullard)

o<-segmented(out.lm, seg.Z=~Rt, psi=list(Rt=c(200,300)), control=seg.control(display=FALSE))

Using the psi option, I have tried the following:

psi = list(x = c(150, 300)) -- OK
psi = list(x = c(100, 200)) -- OK
psi = list(x = c(200, 300)) -- OK
psi = list(x = c(100, 300)) -- OK
psi = list(x = c(120, 150, 300)) -- error 1 below
psi = list(x = c(120, 300)) -- OK
psi = list(x = c(120, 150)) -- OK
psi = list(x = c(150, 300)) -- OK
psi = list(x = c(100, 200, 300)) -- error 2 below

(1) Error in segmented.lm(out.lm, seg.Z = ~Rt, psi = list(Rt = c(120, 150, :
only 1 datum in an interval: breakpoint(s) at the boundary or too close

(2) Error in diag(Cov[id, id]) : subscript out of bounds

I have already listed my data at this question, but as a guide the limits on the x data are about 0–400.

A second question that pertains to this one is: how do I actually fix the breakpoints using this segmented package?

Answer 1

The issue here seems to be poor error trapping in the segmented package. Having a look at the code for segmented.lm allows a bit of debugging. For example, in the case of psi = list(x = c(100, 200, 300)), an augmented linear model is fitted as shown below:

lm(formula = Tem ~ Rt + U1.Rt + U2.Rt + U3.Rt + psi1.Rt + psi2.Rt + 
    psi3.Rt, data = mf)

Call:
lm(formula = Tem ~ Rt + U1.Rt + U2.Rt + U3.Rt + psi1.Rt + psi2.Rt + 
    psi3.Rt, data = mf)

Coefficients:
(Intercept)           Rt        U1.Rt        U2.Rt        U3.Rt      psi1.Rt        
   15.34303      0.04149      0.04591    742.74186   -742.74499      1.02252       
   psi2.Rt      psi3.Rt  
        NA           NA  

As you can see, the fit has NA values which then result in a degenerate variance-covariance matrix (called Cov in the code). The function doesn’t check for this and tries to pull out diagonal entries from Cov and fails with the error message shown. At least the first error, although perhaps not overly helpful, is caught by the function itself and suggests that the break-points are too close.

In the absence of better error trapping in the function, I think that all you can do is adopt a trial and error approach (and avoid break points which are too close). For example, psi = list(x = c(50, 200, 300)) seems to work ok.