Dear all,
I have a statistical question. Suppose that I collect data on
N individuals, on k items. E.g., how well individual i answers question
#j. My response is continuous. I am interested in
(i) assessing the strength of correlation between the k questions
(ii) `deconvolving' the `common signal' for the k questions, from the
`question-specific' signal.
1. Do you have any advice on approaching the problem, and possible
references?
2. For (i), the determinant det(R) of the sample correlation matrix for
the k items gives a 1-number summary of the strength of correlation.
Bartlett 1954 has proposed a test for noncorrelation (R=I) based on
det(R). I would be interested in any insight of how good a measure
of correlation det(R) is, and whether people have looked at CI's for R,
distributions under a correlated model, etc.
3. Related to (ii), suppose now that I have two such N x k tables, i.e.
the same N people x k questions, measured at two points in time. I'd like
to compare the strength of correlation between the two tables, i.e. some
kind of test based on det(R1)/det(R2).
Any insight is warmly welcome.
Thanks,
Florin
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Florin Vaida
Assist Prof, Dept of Biostatistics
Harvard School of Public Health
655 Huntington Ave Boston MA 02115
Tel (617) 432-2914
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