@ Jan Boehnke, Thanks a lot for your response and initiating the discussion with raising some fundamental issues that may be potentially related to the problem that I am facing.

I agree with you that if some items are highly correlated then it may be because of similarity of the psychological content and thus some may be dropped. I would like to invite your view about what value of inter-item correlation should be considered high suggesting considerable overlap of the content. In my case the highest correlation observed is around .7 and thus reflecting an overlap of around 49 % variance and the remaining 51% variance (including both specific and error) may be considered unique.

Here I would like to share the fact that I am evaluating the psychometric properties of the Hindi version of already validated measure and thus at this stage I am not thinking of dropping the items. I am waiting for more data so that I can run a CFA and then take the final decision about retaining/rejecting items.

Further, I would also like to share that the problem of near zero determinant remains even I dropped those items that were highly correlated.

To felicitate the discussion, I would like to share that I tried to compute alpha coefficient of other measures having larger number of items with lower variance and encountered the same message that the determinant is near zero. For instance, the reliability analysis of SCL-90-R was associated with same problem. I guess that the problem is somehow related with the larger number of items with lower variance. But still I am not able to learn how to cope up with this problem. If this problem will be present one cannot compute the SMC (squared multiple correlation)- an index of item reliability.

@Professor Pandey. If one wants to compute the reliability of the testscore using Cronbach's alpha reliability coefficient, one needs only the covariance matrix and the number of items.

http://en.wikipedia.org/wiki/Cronbach's_alpha

I do not see what the correlation matrix has to do with it. Why standardize the item scores?

Om Shanti Shanti Shanti!

@ H. Kelderman. Hari Om Tat Sat

Thanks for your comments. Actually I am interested in getting the SMC (squared multiple correlation) of each item as an index of item reliability. And for this a near zero determinant will create problem particularly in inversion of the matrix. In view of this, I have requested the esteemed members to help me in this regard.

Om Shanti

You may want to use regularized regression analysis to obtain the statistic in this case. See section 3.4 of Hastie et al.: http://www-stat.stanford.edu/~tibs/ElemStatLearn/

I recently got an error message stating ( the correlation matrix is ill conditioned and the determinant of the correlation is equal to zero. The maximum number of principle components that can be extracted will be equal to the number of positive eigenvalues for the matrix.

I then got advise from the net that one can actually lower all correlations in the correlation matrix by adding a small constant to the diagonal of the matrix, and then restandardizing it. I am quite knew completing this.. However i wanted to find out from you fello researchers how does one lower all correlations as indicate above.