On Dec 13, 2010, at 9:21 PM, 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.

Some sort of linearized approximation of a rotation matrix?

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

Now I want to find the values for XScale, YScale and RotAngle

... that does _what_? Minimize the sum of squares of dY and dX?



Length(dX)==length(dY)==length(X)==length(Y)==number of measured sites on a
wafer

So dY and dX are measured and X and Y are measured how many times? And are we doing this for several different wafers so that we need to have nested models that incorporate an error term for each wafer? (And if that is the case this may need to be transferred to the mixed- models mailing list or at the very least answered by someone with a better ax swing for such complexities that I can wield.)

--
David


Hope this clarifies...


-----Original Message-----
From: David Winsemius [mailto:dwinsem...@comcast.net]
Sent: Monday, December 13, 2010 6:06 PM
To: Bastiaan Bergman
Cc: r-help@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 Winsemius, MD
West Hartford, CT

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