Re: Random Grids

Travis Gee (
Wed, 7 Jan 1998 14:14:33 -0500 (EST)

Richard Bell sez:
> 2. But you do raise an interesting question: how do we know if a grid is
> simply random data? Neither principal components or cluster analysis will
> detect this. My feeling is that we would need to look at simpler
> statistics. Or perhaps we don't really want to know the answer.

Bootstrapping and jackknifing have been used in FA, etc. to put error
bars around estimates, and these could be applied to the grid to
determine relative deviation from zero simply by re-estimating
parameters a number of times and looking at the empirical sampling
distributions using the usual analyses. Do they hover around zero or
away from zero?

Another sort-of-related that has intrigued me is "to what extent is the
structure dependent on the elements and constructs included in the
analysis?" There are two ways of the matrix, and it seems to me that
something like jackknifing could be used, dropping an element and a
construct pair in each of 15x15=225 slightly-different matrices, by
assigning missing values to each, re-computing similarity coefficients
(matches, phi or whatever) and running an INDSCAL or ALSCAL on the
lot. The overall structure would emerge as basically similar to the
original, but the solutions with high "weirdness" would reveal which
combinations are necessary to the space by the degree of distortion
required to fit the matrix.

Just some "random" thoughts ;>


Travis Gee () ()
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"In science, the more we know the more extensive the
contact with nescience." -Spencer