This is a common theme of educational testing and is commonly addressed with
loglinear models. The method of analysis is commonly called Rasch Analysis
after the Danish statistician who developed the model. Software has been
developed for the specific analysis of these models. Do a Google search on
Rasch analysis.
Florin Vaida wrote:
> 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
>
> ============================
> 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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