Ones and zeroes can be any level of measurement. However if you want to use
a coefficient specifically oriented to binary data then when you click on
'create distances from data' also click on the 'Measure' button and you
will bring up a menu that enables you to choose a coefficient for binary
data. Alternatively if you click on 'Paste' instead of 'OK' you will see
the syntax and see that SPSS is using the Proximities module to produce the
coefficients. What you are currently creating (by default) are
inter-element distances so it is comforting that you are getting the same
answers as with the OMNIGRID distances.
The issue of symmetry and conditionality applies to these inter element
distances matrices, not the data. Distance matrices are symmetrical, and
the conditionality should be matrix. There are no rules for interpreting
S-stress, but there were some attempts in the 70's to estimate what values
for stress would be found from random data. The best estimate (from Spence,
1979) is
Random data Stress = a0 + a1*D + a2*N + a3*lnD + a4*sqrt(lnN)
where D is the number of dimensions, N is the number of variables, ln is
the natural logarithm, sqrt is the square roots and the a coefficients are
a0 = - 524.25
a1 = 33.80
a2 = -2.54
a3 = -307.26 &
a4 = 588.35
The expect value for 12 points in 2 dimensions is about .227 and the
standard error is about .005 so your results are better than would be
expected from random data - but not by much - I wouldn't be writing to my
mum about them. Unfortunately these results were only derived for a single
grid, we have no idea what happens with replicated or weighted solutions
(though I suspect it still holds - sort of).
>Query 2:
>I am unclear as to the procedure to be completed in order to get
>Replicated MDS. I am using SPSS for Windows 95 and am not familiar with
>the 'old' syntax.
I am not sure why you are wanting to use replicated mds - since this will
only find a common solution and show differences between the grids in the
stress values. However if you want to do it you should simply put the
variable that is the indicator of which gris is while into the 'Individual
Matrices for' box. A solution that would enable you to get measures of the
differences between grids would be weighted MDS, which would show how each
grid weights the dimensions of the common solution. To do this click the
'Model' button, and then under 'Scaling Model' on the next menu, click on
'Individual differences Euclidean distance'. Comparing of the weights is
not easy however (eg through ANOVA) unless you either used the 'flattened
subject weights' (which I find useless) or switch the conditionality from
Matrix to Unconditional (which Forrest Young, the author of ALSCAL, the
scaling program, doesn't like, but others do)
Hope this is of some help
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