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Re: Correct way to normalize an rmsd-based distance metric used in
repeated trials of pairs
Posted:
Apr 8, 2012 4:12 AM
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On Apr 7, 6:19 pm, djh <halitsk...@att.net> wrote:
> I think I see what has to be done mathematically, but don't know
> how to express it statistically. I think it boils down to a four
> predictor logistic model, but I'm not sure.
>
> Each input pair can not only be characterized by two values (vi,vj)
> of our current quantized variable v, but also by two values (ci,cj),
> where c is the new "count" variable I mentioned in my last couple of
> posts. And similarly for each output pair.
>
> So mathematically, our upper-triangular 10x10 matrix V=(vi,vj) is
> actually a matrix of matrices, i.e. each cell (vi,vj) of V is a
> matrix Cij = (cijp,cijq), where p and q are values of C.
For each pair of objects, we arbitrarily assign the 'i' and 'j'
labels so that vi <= vj. But object i has C = ci, and object j has C
= cj, and you haven't said if any special relation holds for those
two C-values by virtue of the corresponding V-values being ordered,
so it sounds like the C matrix in each cell of the upper triangular
V matrix is full square, giving 55*n^2 cells in the design, where
'n' is the number of different values of C.
Note: We've been talking of matrices, but in principle both V (i.e.,
U) and C could be continuous, in which case the input would no longer
be summary counts n0 and n1, but individual 0s and 1s.
>
> I think this boils down to constructing a four-predictor model with
> predictors vi,vj,cp,cq, but again, am not sure.
Right, where cp is the value of C for the object whose V is vi,
and cq is the value of C for the object whose V is vj.
>
> If/when you have a chance, please advise whether I'm looking at this
> correctly. If so, I'll have to write a little more PERL to generate
> the numbers, but I think it may be worth it. I'm in the process of
> hand-tallying a couple of Cij matrices to see what they look like,
> and they really seem to be quite orderly ...
>
> One other question - would it be preferable to run some two-predictor
> models using just cp,cq before trying to combine these predictors
> with the vi,vj predictors? Or do you always have to run all relevant
> variables "together"?
In general, you always need to put all the predictors in together.
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