Piecewise linear regression in R (segmented.lm) - r

Question

I appreciate any help to make segmented.lm (or any other function) find the obvious breakpoints in this example:
data = list(x=c(50,60,70,80,90) , y= c(703.786,705.857,708.153,711.056,709.257))
plot(data, type='b')
require(segmented)
model.lm = segmented(lm(y~x,data = data),seg.Z = ~x, psi = NA)
It returns with the following error:
Error in solve.default(crossprod(x1), crossprod(x1, y1)) :
system is computationally singular: reciprocal condition number = 1.51417e-20
If I change K:
model.lm = segmented(lm(y~x,data = data),seg.Z = ~x, psi = NA, control = seg.control(K=1))
I get another error:
Error in segmented.lm(lm(y ~ x, data = data), seg.Z = ~x, psi = NA, control = seg.control(K = 1)) :
only 1 datum in an interval: breakpoint(s) at the boundary or too close each other

Answer 1

A nice objective method to determine the break point is described in Crawley (2007: 427).
First, define a vector breaks for a range of potential break points:
breaks <- data$x[data$x >= 70 & data$x <= 90]
Then run a for loop for piecewise regressions for all potential break points and yank out the minimal residual standard error (mse) for each model from the summary output:
mse <- numeric(length(breaks))
for(i in 1:length(breaks)){
piecewise <- lm(data$y ~ data$y*(data$x < breaks[i]) + data$y*(data$x >= breaks[i]))
mse[i] <- summary(piecewise)[6]
}
mse <- as.numeric(mse)
Finally, identify the break point with the least mse:
breaks[which(mse==min(mse))]
Hope this helps.