How to perform Broken-line regression analysis in R? - r

Question

I have the following data:
Treatment Dose Value
FeSo4 200 104.17
TQ1 6 98.17
TQ2 9 92
TQ3 12 86.67
TQ4 15 77.33
TQ5 18 71.33
TQ6 21 74.83
TQ7 24 82.17
How can I do Broken-line regression analysis of this data in R to get the graph as below:

Answer 1

The best way to fit linear models by segments in R is to use CRAN package segmented.
In what follows, I have created a new column, coercing column Treatment from class factor to its integer codes.
library(segmented)
df1$Num <- as.integer(df1$Treatment)
fit <- lm(Value ~ Num, df1)
summary(fit)
seg <- segmented(fit, seg.Z = ~Num, psi = 6)
plot(Value ~ Num, df1) # plot the points
plot(seg, add = TRUE) # plot the broken line
abline(v = seg$psi[2]) # plot the vertical at the breakpoint
Data.
df1 <- read.table(text = "
Treatment Dose Value
FeSo4 200 104.17
TQ1 6 98.17
TQ2 9 92
TQ3 12 86.67
TQ4 15 77.33
TQ5 18 71.33
TQ6 21 74.83
TQ7 24 82.17
", header = TRUE)

Answer 2

A different approach is to first find the threshold and then fit a regular lm() model:
library(SiZer)
df <- read.table(text = "
Treatment Dose Value
FeSo4 200 104.17
TQ1 6 98.17
TQ2 9 92
TQ3 12 86.67
TQ4 15 77.33
TQ5 18 71.33
TQ6 21 74.83
TQ7 24 82.17
", header = TRUE)
df$Num <- as.integer(df$Treatment)
thr.pwl = piecewise.linear(df$Num, df$Value,
middle = 1, CI = FALSE,
bootstrap.samples = 1000, sig.level = 0.001)
thr.pwl
[1] "Threshold alpha: 6.30159931424453" #This is the threshold you need
[1] ""
[1] "Model coefficients: Beta[0], Beta[1], Beta[2]" #The estimates here are the same as in model.pwl, however, with lm() you can include also other independent variables
(Intercept) x w
111.48333 -6.63000 13.97001
model.pwl <- lm(Value ~ Num*(Num >= 6.30) + Num*(Num < 6.30),
data = df)
summary(model.pwl)
And you can plot it as:
plot(thr.pwl)
abline(v = thr.pwl$change.point)
However, with piecewise.linear() you can only us one threshold, while with segmented() more of them.