[R] Siegel nonparametric regression / mblm package

[Roger Koenker]

A quick look at the code for Siegel in mblm reveals that it is extremely inefficient, but it seems to be correct.
One “explanation” for this behavior, presuming that we haven’t overlooked something more basic, is that such
high breakdown estimates sacrifice some efficiency, that is to say, they are more variable than other methods
when the data is well behaved, and of course, the Galton data is famously “almost Gaussian”.

> On Feb 11, 2019, at 12:47 PM, Marco Besozzi <marco.beso48 using 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 using illinois.edu <mailto:rkoenker using 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 using gmail.com <mailto:marco.beso48 using 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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> 


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