[R] piecewise regression and lm() question

[Goldschneider, Jill]

I was playing with some examples of piecewise regression using lm() and have come across a behavior I'm uncertain about.
Below is simple 3-segment dataset.  I compare predicted output of a model created by one call to lm() to that of 3 models created by 3 calls to lm().
In case A and B, the results are the same.  However, in case C the results differ for the middle segment.
Is the output of lm() for case C to be expected or not and if so, why?
Thank you,
Jill

set.seed(133)
y <- c(21:30, rep(15,10), 10:1) + runif(30, -2, 2)
x <- 1:30

# Case A: 3 segments, each fit with a constant value
plot(x, y)
# 3 different lm fits
p.c3 <- c(predict(lm(y[1:10]~1)), predict(lm(y[11:20]~1)), predict(lm(y[21:30]~1)))
lines(x, p.c3, col="red")
# piecewise via lm
p.lm1 <- predict(lm(y ~ I(x<=10) + I(x>10 & x<=20) + I(x>20)))
lines(x, p.lm1, col="blue")
max(abs(p.c3-p.lm1))

# Case B: 3 segments, each fit with a line
plot(x, y)
# 3 different lm fits
p.c3 <- c(predict(lm(y[1:10]~x[1:10])), predict(lm(y[11:20]~x[11:20])), predict(lm(y[21:30]~x[21:30])))
lines(x, p.c3, col="red")
# piecewise via lm
p.lm1 <- predict(lm(y ~ (x<=10)*x + (x>10 & x<=20)*x + (x>20)*x))
lines(x, p.lm1, col="blue")
max(abs(p.c3-p.lm1))

# Cast C: 3 segments - the middle fit with a constant value, the outer by a line
plot(x, y)
# 3 different lm fits
p.c3 <- c(predict(lm(y[1:10]~x[1:10])), predict(lm(y[11:20]~1)), predict(lm(y[21:30]~x[21:30])))
lines(x, p.c3, col="red")
# piecewise via lm
p.lm1 <- predict(lm(y ~ (x<=10)*x + I(x>10 & x<=20) + (x>20)*x))
lines(x, p.lm1, col="blue")
max(abs(p.c3-p.lm1))
## the single call to lm does not have a constant value fit to the middle section
plot(x, p.c3-p.lm1 )



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