# [R] ML optimization question--unidimensional unfolding scalin g

Peter Muhlberger peterm at andrew.cmu.edu
Thu Nov 3 19:02:16 CET 2005

```Hi Spencer:  Just realized I may have misunderstood your comments about
branching--you may have been thinking about a restart.  Sorry if I
misrepresented them.

See below:

On 11/3/05 11:03 AM, "Spencer Graves" <spencer.graves at pdf.com> wrote:

> Hi, Andy and Peter:
>
>  That's interesting.  I still like the idea of making my own local
> working through the code.  I haven't used "debug", but I think I should
> try it, because some things occur when running a function that don't
> occur when I walk through it line by line, e.g., parsing the "call" and
> "..." arguments.
>

Debug's handy tho I think it is line by line.

>  Two more comments on the original question:
>
>  1.  What is the structure of your data?  Have you considered
> techniques for Multidimensional Scaling (MDS)?  It seems that your
> problem is just a univariate analogue of the MDS problem.  For metric
> MDS from a complete distance matrix, the solution is relatively
> straightforward computation of eigenvalues and vectors from a matrix
> computed from the distance matrix, and there is software widely
> available for the nonmetric MDS problem.  For a terse introduction to
> that literature, see Venables and Ripley (2002) Modern Applied
> Statistics with S, 4th ed. (Springer, "distance methods" in sec. 11.1,
> pp. 306-308).
>

I was looking for something on MDS in R, that'll be handy!

The data structure is a set of variables (say about 6) that I have reason to
believe measure an underlying dimension.  I suspect that several of the
variables are unfolding--that is, they have their highest value for some
point on the scale and fall off w/ distance from that point in either
direction.  The degree of fall-off may vary depending on the variable.  Some
seem to fall off very rapidly, others not.  A couple variables probably
monotonically increase w/ the underlying scale, so they don't unfold.  I can
construct a distance matrix consisting of distances between these variables.

Do you think MDS might be able to handle an arrangement like this, w/ some
values folded about a scale point and with drop-off varying between
variables?  The distances between the variables do not map in any
straightforward way into distances on the underlying scale because of
folding and non-linearity.

>  2.  If you don't have a complete distance matrix, might it be
> feasible to approach the problem starting small and building larger,
>

Not sure I follow, but I do have a complete distance matrix of distances
between the variables.

>  spencer graves

Thanks,

Peter

```