Instability of statistical factor analysis
Author:
Steven P. Ellis
Translated by:
Journal:
Proc. Amer. Math. Soc. 132 (2004), 18051822
MSC (2000):
Primary 62H25; Secondary 65D10
Published electronically:
January 7, 2004
MathSciNet review:
2051145
Fulltext PDF Free Access
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Abstract: Factor analysis, a popular method for interpreting multivariate data, models the covariance among variables as being due to a small number (, ) of hidden variables. A factor analysis of can be thought of as an ordered or unordered collection, , of linearly independent lines in . Let be the collection of data sets for which is defined. The ``singularities'' of are those data sets, , in the closure, , at which the limit, , does not exist. is unstable near its singularities. Let be the direct sum of the lines in . determines a plane bundle, , over a subset, , of . If and is rich enough, ordered or, at least if or 3, unordered, must have a singularity at some data set in . The proofs are applications of algebraic topology. Examples are provided.
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Additional Information
Steven P. Ellis
Affiliation:
New York State Psychiatric Institute and Columbia University, Unit 42, NYSPI, 1051 Riverside Dr., New York, New York 10032
Email:
ellis@neuron.cpmc.columbia.edu
DOI:
http://dx.doi.org/10.1090/S0002993904072727
PII:
S 00029939(04)072727
Keywords:
Vector bundle,
maximum likelihood,
principal components
Received by editor(s):
December 3, 2001
Published electronically:
January 7, 2004
Additional Notes:
This research is supported in part by United States PHS grants MH46745, MH60995, and MH62185.
Communicated by:
Richard A. Davis
Article copyright:
© Copyright 2004
American Mathematical Society
