[R] multivariate multi regression / aligning objects anything in bio or mapping?

[Mike Marchywka]

----------------------------------------
> From: pdalgd at gmail.com
> Date: Tue, 14 Dec 2010 13:50:27 +0100
> To: Bastiaan.Bergman at wdc.com
> CC: r-help at r-project.org
> Subject: Re: [R] multivariate multi regression
>
>
> On Dec 14, 2010, at 03:21 , Bastiaan Bergman wrote:
>
> > That doesn't work, one would get two different answers depending on the
> > order of execution.
> >
> > The physics is: Overlay error on a Silicon wafer. One wafer has many flash
> > fields, each flash field has multiple locations where the overlay error is
> > measured (as: dX,dY offset). If one contemplates that the error is caused by
> > a rotation of the flash field then we can say (dX,dY)=(-Y,X)*RotAngle. If in
> > addition we have a scaling error: (dX,dY)=(X*XScale,Y*YScale) than the total
> > model is:
> > dX~X*XScale-Y*RotAngle
> > dY~Y*YScale+X*RotAngle
> >


First of course if you have a model it would help to get the equations right
for tanslation, scale, and rotation around an arbitrary origin. If you
can live with 3D, there may be something in the bio packages for aligning
molecules with no assumptions about their relative initial orientations.
Anyone know off hand if objection alignment exists in any bio or mapping
packages? I would imagine related tasks come up in building a coherent map
out of overlapping pieces, something which may have significant support too. 






> > Now I want to find the values for XScale, YScale and RotAngle
> > Length(dX)==length(dY)==length(X)==length(Y)==number of measured sites on a
> > wafer
> >
> > Hope this clarifies...
>
> Not completely, but I can see the general picture.
>
> I think the main thing is to rewrite the formula as
>
> dX = XScale * X + YScale * 0 + RotAngle * (-Y) + eX
> dY = XScale * 0 + YScale * Y + RotAngle * X + eY
>
> (where eX and eY are noise terms)
>
> Then string together all your data pairs as
>
> dX1
> dY1
> dX2
> dY2
> ...
>
> and the corresponding design matrix
>
> X1 0 -Y1
> 0 Y1 X1
> X2 0 -Y2
> 0 Y2 X2
> ...
>
> This sets up the joint linear model that you want. (Technically, it could be easier to put all the dX's first, then all the dY's, though.)
>
> The remaining question is what you assume about the eX and eY terms. If they can be assumed to be independent and have the same variance, you're done. If they are correlated and/or have different variance, then I think you need to look in the direction of lme() with a suitable variance function.
>
>
>
> >
> >
> > -----Original Message-----
> > From: David Winsemius [mailto:dwinsemius at comcast.net]
> > Sent: Monday, December 13, 2010 6:06 PM
> > To: Bastiaan Bergman
> > Cc: r-help at r-project.org
> > Subject: Re: [R] multivariate multi regression
> >
> >
> > On Dec 13, 2010, at 8:46 PM, Bastiaan Bergman wrote:
> >
> >> Hello,
> >>
> >>
> >> I want to model my data with the following model:
> >>
> >>
> >> Y1=X1*coef1+X2*coef2
> >> Y2=X1*coef2+X2*coef3
> >>
> >>
> >> Note: coef2 appears in both lines
> >>
> >> Xi, Yi is input versus output data respectively
> >>
> >> How can I do this in R?
> >>
> >> I got this far:
> >>
> >> lm(Y1~X1+X2,mydata)
> >>
> >> now how do I add the second line of the model including the cross
> >> dependency?
> >
> > The usual way would be to extract coef2 from the object returned from
> > the first invocation of lm(...) and use it to calculate an offset
> > term in a second model. It would not have any variance calculated
> > since you are forcing it to be what was returned in the first model.
> > Now, what is it that you are really trying to do with this procedure?
> >
> > --
> > David.
> >
> >
> > David Winsemius, MD
> > West Hartford, CT
> >
> > ______________________________________________
> > R-help at r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
>
> --
> Peter Dalgaard
> Center for Statistics, Copenhagen Business School
> Solbjerg Plads 3, 2000 Frederiksberg, Denmark
> Phone: (+45)38153501
> Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com
>
> ______________________________________________
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