[R] Question on broken-line regression: 'segmented' or alternative
Benedikt Drosse
drosse at mpipz.mpg.de
Sat Jan 12 11:13:25 CET 2013
Dear R-Users,
I have a question concerning the determination of breakpoints and
comparison of slopes from broken-line regression models. Although this
is rather a standard problem in data analysis, all information I
gathered so far, did not answer my questions.
I added a subsetted example of my data. Basically it is a timeseries of
recorded phenotypes in three different groups of plants.
You will see in the plot that the phenotype between groups behaves
differently over time. Plotted data of Group 3 look like a nice linear
relationship between phenotype (y) and time (x). Group 1 seems to have 1
breakpoint (at x=31) and Group 3 has 2 breakpoints (at x=c(14,31)) in
the data.
1. I am very interested in finding the breakpoints (x-values), where the
slope of a regression line changes. In the plot I estimated the
break-points by eye, subsetted the data and performed linear regression
on the subsets for each group. However, this is not the way I want to
go, since I would like to have some reasonable criteria (better than my
eye) to determine breakpoints.
2. Additionally I am interested in testing, whether the slopes of
(partial-)regression lines between groups are different from each other.
Considering my questions, the 'segmented' package should exactly fit my
needs. The problem I have is, that on the one hand I would also like to
compare slopes of regression lines, which do not have breakpoints (e.g
group 3 of the example) to lines, which have breakpoints (group 1 and
2). This seems to be not possible with the 'segmented' package.
On the other hand the 'segmented' package seems to have a poor
error-reporting, so it is very hard for me to figure out, what is going
wrong in the analysis (see example).
Can you think of any other way/procedure/package I could use to analyze
my data? Hopefully you can also give me a clue on how to proceed with
the analysis, when the error of the segmented()-function in the creation
of the covariance-matrix occurs.
I would be grateful for any comment on how to determine breakpoints and
compare slopes of regression lines in a different way than subsetting
the data by hand and regress the subsetted parts as I did it for the
example plot. Thanks to anyone, who has an idea, already. Sorry for the
long example code.
Best regards,
Benedikt
#Start of Code
library(car)
library(segmented)
#Data file:
#Timescale:
x <-
c(0,0,0,3,3,3,3,3,3,6,6,6,9,9,9,14,14,14,17,17,17,20,20,20,24,24,24,28,28,28,31,31,31,34,34,34,38,38,38,45,45,45,0,0,0,3,3,3,3,3,3,6,6,6,9,9,9,14,14,14,17,17,17,20,20,20,24,24,24,28,28,28,31,31,31,34,34,34,38,38,38,45,45,45,0,0,0,3,3,3,7,7,7,9,9,9,13,13,13,13,13,16,16,16,20,20,20,24,24,24,28,28,28,34,34,34,41,41,41,50,50,50)
#y-data for three groups (t1, t2, t3):
t1 <-
c(41,35,38,43,47,46,50,41,47,74,61,58,72,87,84,89,114,93,113,99,105,106,98,200,170,145,153,187,202,195,198,177,195,288,274,233,320,348,428,545,520,549)
t2 <-
c(44,40,38,57,42,47,42,57,40,71,75,64,70,83,88,115,95,106,132,145,115,192,172,190,273,300,250,403,392,343,400,402,444,NA,NA,NA,NA,NA,NA,430,430,459)
t3 <-
c(41,35,38,39,43,47,58,33,45,67,60,70,64,78,78,67,62,78,79,71,93,86,82,105,96,102,131,126,124,112,100,133,170,161,163,154,178,185)
group <- as.factor(c(rep(1, times=length(t1)), rep(2,
times=length(t2)), rep(3, times=length(t3))))
data <- data.frame(group, x=x, y=c(t1,t2,t3))
#Groupwise plot of datapoints vs time:
scatterplot(y~x*group, data=data, smooth=FALSE, reg.line=FALSE,
legend.coords="topleft")
#Regressions for group 1 with 1 breakpoints (red, dashed line)
reg_1.1 <- lm(data[which(data$x<=30 &
data$group==1),3]~data[which(data$x<=30 & data$group==1),2])
abline(reg_1.1, col="black")
reg_1.2 <- lm(data[which(data$x>=30 &
data$group==1),3]~data[which(data$x>=30 & data$group==1),2])
abline(reg_1.2, col="black")
#Regressions for group 2 with 2 breakpoints (black, solid line)
reg_2.1 <- lm(data[which(data$x<=14 &
data$group==2),3]~data[which(data$x<=14 & data$group==2),2])
abline(reg_2.1, col="red", lty=2)
reg_2.2 <- lm(data[which(data$x>=14 & data$x<45 &
data$group==2),3]~data[which(data$x>=14 & data$x<45 & data$group==2),2])
abline(reg_2.2, col="red", lty=2)
reg_2.3 <- lm(data[which(data$x>=31 & data$x<=45 &
data$group==2),3]~data[which(data$x>=31 & data$x<=45 & data$group==2),2])
abline(reg_2.3, col="red", lty=2)
#Regression for group 3 without breakpoints (green, solid line)
reg_3.1 <- lm(data[which(data$group==3),3]~data[which(data$group==3),2])
abline(reg_3.1, col="green", lty=1)
#Segmented package to estimate breakpoints and determine slopes for
group2 and 3:
subset_data <- subset(data, subset=data$group!=3)
names(subset_data) <- c("sub_group", "sub_x", "sub_y")
attach(subset_data)
X <- model.matrix(~0+sub_group)*sub_x
time.1 <- X[,1]
time.2 <- X[,2]
time.3 <- X[,3]
olm <- lm(sub_y~0 + sub_group + time.1 + time.2)
os <- segmented(olm, seg.Z= ~ time.1 + time.2,
psi=list(time.1=c(14,30), time.2=40))
#End of code
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