Re: FA vs. PCA and grouped vs. non-grouped

1. I'm familiar with the SAS Polychor macro. It's basically a way to
repeatedly invoke PROC FREQ with the PLCORR option. (Much simpler, by
the way, is PRELIS, a program that comes with LISREL; PRELIS will
calculate a correlation matrix, including polychoric and tetrachoric
correlations, automatically using the appropriate formulas, for all
pairings of interval, ordinal, and binary items).

2. The problem with factor scores I referred to is that when you
supply a correlation matrix that contains polychoric or tetrachoric
correlations, PROC FACTOR doesn't know this. There is no problem when
it comes to estimating factor loadings. But it doesn't work for
estimating factor scores. This example explains why:

a. let y1 and y2 be two observed binary variables (say, below/above
average income);

b. let x1 and x2 be two continuous variables, the latent "precursors"
(pre-dichotomized versions) of y1 and y2 (say, income in dollars);

c. the tetrachoric correlation, rho(y1, y2) estimates the Pearson
correlation r(x1, x2);

d. suppose you place this value in a correlation matrix; and

e. you factor analyze the matrix.

f. the resulting factor loadings for these variables would apply,
strictly speaking, to the hypothetical continuous variables x1 and
x2--not your actual variables, y1 and y2.

g. that's fine if you're mainly interested in identifying constructs
and their structure,

h. but it doesn't let you correctly calculate factor scores from the
factor loadings. The factor loadings relate to x1 and x2, but would be
applied in factor-score calculation to y1 and y2, giving incorrect
results.

3. I tend to agree with what Art suggested in his last post about
preferring unit-weighting to automatically calculated factor scores.

--
John Uebersax PhD

.

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