> A question re principal component analysis of grids (I'm no doubt
> revealing my statistical naivete, but what the hell): are the factors
> conceptualized as unverbalized superordinate constructs? If not, what
> are they? I confess to a certain discomfort with entities that have no
> non-statistical correlate. I'll probably get over it one of these days...
>
> Tim Connor
>
They are just another way of construing the data in the grid. That
_MAY_ be a useful way of construing the construing system of the
respondent but it may not. The issues are not "statistical" if we're
being pedantic (preemptive? 8-)) about that construct i.e. they do
not rest on any probability construct system. They are mathematical
in that they have the odd property of exactly reproducing the data in the grid
if all the components are used and of offering the best
approximations in the chosen number of independent Euclidean
dimensions when fewer than all are used. The analogy I use to
understand them is of recovering a 2-D mapping if I were given a set
of measurments of positions of cities on a map of a country. The
component analysis of a whole lot of measurements should reveal two
large components and a sprinkling of smaller ones reflecting
curvature of the earth or inaccuracies in measurement. That's not
exactly recovering a superordinate system, really just noting
redundancy in one set of coordinate measurements that allows them to
be more economically expressed in another of lower dimension.
That's nice for those of us who think visually and spatially but
discomforting if you are looking for a non-mathematical "thing"
beneath them. There are all sorts of caveats about what might
have been going on in the mind of the respondent and how the
numbers you have may, of course, be a very limited angle onto
that and, of course, my 2D mapping analogy is much simpler than the
real situation.
I'm chary of regarding them as indicative of unverbalised
superordinate constructs but certainly when you do find that a very
few components account for a very large proportion of the variance in
the grid then that may be a useful idea to explore with the
respondent if you want to get non-mathematical. There are good ways
of approaching this with Mildred Shaw and also Richard Bell's works
on grids e.g. pointing out that some constructs seem to be highly
associated in the elements rated and focussing in on elements with
discrepant ratings or asking about perceived similarities or
differences between the constructs or asking for elements that do
tease them apart, asking for implications or equivalences etc.
Hope this helps,
Chris
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