Re: polychoric correlations

A comment on one point.

On 2 Nov 2005 08:48:59 -0800, "John Uebersax" <jsuebersax@xxxxxxxxx>
wrote:

[snip, much]
> Many Variables
>
> As Rich pointed out, 177 variables with N=200 is probably too many to
> expect good results from factor analysis. Here's an alternative:
> pre-process the variables by identifying pairs or sets of highly
> correlated ones. For each set, designate one variable the "exemplar."
> Then omit from the factor analysis all variables in each set except the
> exemplar.
[ snip, rest]

That's one solution which is sometimes good.

Or, instead of the "exemplar", you could use the
average of the several items that are highly correlated,
instead of any one of them.

This reminds me of my concern, though, with all those
"missing" values. Using the average of the non-missing
is not bad when the means are all the same, but you can
get into trouble when what's missing is responsible for
high (or low) scores. Two alternatives are: Substituting
the item's average, or using regression for substitution.
Both of those can be wrong when the item is not "missing
at random."

But this is a problem for the eventual use of the result,
too. How good is a computed "score" for someone when
it is based on a fraction of the items that were supposed
to be there?

[ ... ]

--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.

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