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> 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>______________________________________________
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