🚀 go-pugleaf

Steve blinkhorn quite correctly points out that phi coefficients ARE pearson
corrs.  When I re-read my own message, I realized that what I'd SAID was phi,
but what I MEANT was phi/phi max, which I've seen lots of people use as
matrix input, but which I believe is indefensible.

In my own experience, the Heywood cases seem to arise from dichotomies with
extreme p's which often yield linear combinations--especially if the ratio
of cases to variables is insufficiently large.  The results are then artifacts
of the dataset and not representative of what's happening in the population.
In reality, this is simply an instance of the "normal problems" Steve mentions.
I can't imagine why anyone would want to use dichotomies that were cut-points
of continuous measures if the continuous data were available, but for some
measures the data are truly dichotomous (gender, living/deceased, domiciled
alone/with others) and are sometimes the best measures at hand.  I have several
reservations though, about using dichotomous dummy variables in anything more
rigorous than cursory exploratory factor analyses.  And that's maybe an idea
that needs to be clarified--we can perhaps allow ourselves more latitude
in exploratory investigations than in confirmatory ones...    John