# Re: measuring change

Tony Downing (a.c.downing@newcastle.ac.uk)
Thu, 27 May 1999 15:54:53 +0100

J.Maxwell Legg wrote:

>Yes there is a problem of assumptions based on the proximity within a 2D
>plot. You will notice that for only two constructs (e.g., latitude and
>longitude) the total variation of the grid vs. the number of elements
>lies on a single plane. The MDS plot within WinGrid uses a stepping
>bandwidth to average its order throughout this total variation while
>spinning the grid across a range of dimensions.
>
>Whereas to pinpoint a geographic location on a map requires a minimum of
>latitude and longitude, Patrick Slater explained to me that these single
>numbered grid ratings each described a knot of many coordinates in a
>multi-dimensional space.
>
>He chose PCA over Factor Analysis as an effective way of untangling that
>knot.

Presumably what you can do to get the distance in a multidimensional space
involving N factors from PCA woould be to save factor scores for the
elements.
(You might have to use a general purpose stats package such as SPsS or
Minitab for the PCA to do this - I'm not sure whether it's an option in the
specialist grid packages). Then use Pythagoras's Theorem, in as many
dimensions as there are factors, to calculate each distance. I haven't done
such a calculation since high school, but it's really simple in principle
and if I weren't in a tearing hurry I'd work it out here and now. Can any
proper maths person chip in and confirm the answer?! Something like the
square root of the sum of the squares of the differences between the scores
on each factor ...

Best wishes,

Tony.

==========================================================================
Tony Downing, M.A., Ph.D.
Lecturer, Dept. of Psychology,
University of Newcastle upon Tyne, NE1 7RU,
UK.

email: A.C.Downing@Newcastle.ac.uk
Phone +44 (0)191 222 6184 Mobile: +44 (0) 468 427 481
Fax: +44 (0)191 222 5622
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