On Feb 11, 2019, at 12:47 PM, Marco Besozzi <marco.beso48 at gmail.com> wrote:
Thank you very much for your reply.
If I have well understood, unfortunately in this way I have lost the only idea I had...
Do you believe that a problem in the R algorithm employed in the package mblm for Siegel regression is possible?
And do you know if Siegel regression is available in a different package? I was unable to find it.
Thanks again!
Best regards.
P.S.: sorry for my bad english...
Il giorno lun 11 feb 2019 alle ore 12:54 Roger Koenker <rkoenker at illinois.edu <mailto:rkoenker at illinois.edu>> ha scritto:
My first thought was also that this was an artifact of the ties, but dithering the data
n <- length(child)
child <- child + runif(n,-.5,.5)
parent <- parent + runif(n,-.5,.5)
and rerunning yields the same discrepancy between the Siegel and other fits. Curiously, both
lmsreg and ltsreg from MASS produce lines that are more steeply sloped than those
of the other methods. Since I stupidly forgot to set.seed(), YMMV.
On Feb 11, 2019, at 10:24 AM, Marco Besozzi <marco.beso48 at gmail.com <mailto:marco.beso48 at gmail.com>> wrote:
I employed the "galton" set of data included in the package "psych". With
the package "mblm" I obtained the Theil-Sen nonparametric regression and
the Siegel non parametric regression, and compared them with the ordinary
least square regression line.
The results of standard regression and Theil-Sen regression are practically
identical. But the Siegel regression seems to have a bias that I cannot
understand. May I ask for a possible explanation? The bias may be related
to the number of ties in the set of data? Here's the code and the image.
Best regards.
Marco Besozzi
# Theil-Sen and Siegel nonparametric regression with package mblm
# comparison with ordinary least squares (parametric) regression
# on galton set of data included in the package psych
#
library(psych)
attach(galton)
library(mblm)
#
reglin_yx <- lm(child ~ parent, data=galton) # ordinary least squares
(parametric) regression
a_yx <- reglin_yx$coefficients[1] # intercept a
b_yx <- reglin_yx$coefficients[2] # slope b
#
regnonTS <- mblm(child ~ parent, data=galton, repeated=FALSE) # Theil-Sen
nonparametric regression (wait a few minutes!)
a_TS <- regnonTS$coefficients[1] # intercept a
b_TS <- regnonTS$coefficients[2] # slope b
#
regnonS = mblm(child ~ parent, data=galton, repeated=TRUE) # Siegel
nonparametric regression
a_S <- regnonS$coefficients[1] # intercept a
b_S <- regnonS$coefficients[2] # slope b
#
# xy plot of data and regression lines
#
windows() # open a new window
plot(parent, child, xlim = c(60,80), ylim = c(60,80), pch=1, xlab="Parent
heigt (inch)", ylab="Chile height (inch)", main="Regression lines
comparison", cex.main = 0.9) # data plot
abline(a_yx, b_yx, col="green", lty=1) # ordinary least squares
(parametric) regression line
abline(a_TS, b_TS, col="blue", lty=1) # Theil-Sen nonparametric regression
line
abline(a_S, b_S, col="red", lty=1) # Siegel nonparametric regression
legend(60, 80, legend=c("Ordinary least squares regression", "Theil-Sen
nonparametric regression","Siegel nonparametric regression"),
col=c("green", "blue", "red"), lty=c(4,4,1), cex=0.8) # add a legend
#
<Siegel.PNG>______________________________________________