piecewise regression in r - r

Question

I have two variables, A and B, that are significantly related if modeled in a piecewise regression. The model has two segments. The problem is that in the plot, the two segments do not connect to one another the way they should: they form a 'nose' at the break point. I've seen in other posts on Stackoverflow that problems with plotting segmented regressions correctly seem widespread.
Here's the dataframe with A and B:
dfrm <- read.table(text=" A B
1 0.04545455 1.3
2 0.09090909 1.1
3 0.13636364 1.6
4 0.18181818 1.8
5 0.22727273 3.4
6 0.27272727 1.8
7 0.31818182 1.9
8 0.36363636 0.7
9 0.40909091 2.9
10 0.45454545 1.2
11 0.50000000 0.8
12 0.54545455 0.7
13 0.59090909 0.6
14 0.63636364 1.7
15 0.68181818 0.7
16 0.72727273 2.0
17 0.77272727 1.2
18 0.81818182 0.5
19 0.86363636 2.8
20 0.90909091 1.0
21 0.95454545 0.5
22 1.00000000 1.0
23 0.06666667 0.2
24 0.13333333 0.6
25 0.20000000 1.6
26 0.26666667 0.4
27 0.33333333 1.7
28 0.40000000 2.5
29 0.46666667 0.5
30 0.53333333 1.5
31 0.60000000 0.4
32 0.66666667 0.3
33 0.73333333 0.2
34 0.80000000 0.2
35 0.86666667 0.7
36 0.93333333 2.2
37 1.00000000 2.3
38 0.05882353 1.4
39 0.11764706 2.7
40 0.17647059 0.7
41 0.23529412 0.2
42 0.29411765 0.8
43 0.35294118 2.9
44 0.41176471 0.4
45 0.47058824 0.5
46 0.52941176 2.1
47 0.58823529 0.4
48 0.64705882 0.6
49 0.70588235 1.0
50 0.76470588 0.3
51 0.82352941 0.9
52 0.88235294 1.4
53 0.94117647 0.6
54 1.00000000 0.4
55 0.10000000 1.7
56 0.20000000 1.4
57 0.30000000 1.5
58 0.40000000 0.6
59 0.50000000 0.4
60 0.60000000 0.5
61 0.70000000 0.4
62 0.80000000 1.0
63 0.90000000 0.8
64 1.00000000 3.0
65 0.03846154 1.5
66 0.07692308 2.7
67 0.11538462 2.2
68 0.15384615 0.6
69 0.19230769 0.7
70 0.23076923 0.5
71 0.26923077 0.5
72 0.30769231 0.6
73 0.34615385 1.2
74 0.38461538 0.8
75 0.42307692 1.8
76 0.46153846 2.1
77 0.50000000 0.6
78 0.53846154 0.7
79 0.57692308 1.3
80 0.61538462 0.4
81 0.65384615 0.7
82 0.69230769 1.2
83 0.73076923 0.8
84 0.76923077 1.2
85 0.80769231 1.0
86 0.84615385 1.4
87 0.88461538 0.9
88 0.92307692 0.8
89 0.96153846 1.7
90 1.00000000 5.8", header=TRUE)
## attach(df) NO, don't use attach and mistrust anyone who tells you differently
model <- lm(B ~ (A < 0.89394)*A + (A >= 0.89394)*A, data=dfrm) # 0.89394 = breakpoint
# Preparing the plot:
a <- sort(unique(dfrm$A))
# Plotting:
plot(B ~ A, data=dfrm)
lines(a, predict(model, list(A=a)), lwd=2, col="blue")
This is the plot:Piecewise regression
How can the two segments be connected cleanly at the break point?

Answer 1

It might be easiest to attempt this with a GAM (Generalized Additive Model), applied via either the GAM package or the mgcv package in R. This technique allows you to fit a non-linear model in stages, smoothing out the joins (or 'knots) between functions. As a bonus, the GAM is basically a GLM anyway so the learning curve should be quite easy.

Answer 2

The nose and the disconnect between the segments may be due to lack of precision in the way the break point is determined.
After re-determining the break point for my data based on the method detailed in Crawley (2007: 427), the two segments perfectly connect.
The steps involved are:
define a vector "breaks" for potential breaks
run a for loop for piecewise regressions for all potential break points and yank out the minimal residual standard error (mse) for each model:
mse <- numeric(length(breaks))
for(i in 1:length(breaks)){
piecewise <- lm(V_indep ~ V_dep*(V_dep < breaks[i]) + V_dep*(V_dep>=breaks[i]))
mse[i] <- summary(piecewise)[6]
}
mse <- numeric(length(breaks))
identify the break point with the least mse:
breaks[which(mse==min(mse))]
fit the model using this break point.