Hi,

I am currently working on a project about new scale construction. My professor has required us to perform an internal consistency analysis (Cronbach's Alpha) based on the pilot data. Initially, we had 30 items, but we need to reduce it to 15 items for the final scale.

During the reliability analysis, I encountered a warning message: "The determinant of the covariance matrix is zero or approximately zero. Statistics based on its inverse matrix cannot be computed and they are displayed as system missing values." Why did this happen, and will it affect my analysis? 

In addition, when looking at the Item-Total Statistics, I noticed that the column for Squared Multiple Correlation is missing. What could be the reason for this, and will it impact my analysis?

Furthermore, I would appreciate it if someone could guide me on how to decide which items should be deleted.

As I am new to using SPSS, I would highly appreciate any assistance. Thank you very much!

Some of your variables (items) are linearly related or almost related. Perhaps, one is (almost) a copy of the other or correlates perfectly, or a linear function of several other ones. Sure, multiple correlation coefficient cannot be computed then. Remove items which are (almost) completely predictable linearly by the other items.

https://stats.stackexchange.com/q/70899/3277

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Kirill Orlov
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Thank you for your reply, Kirill.

As you suggested, I am considering removing predictable items, but I need guidance on how to make the decision. I have several thoughts, but I am not sure if they are correct. Firstly, I believe I should remove items with low corrected item-total correlations, such as prs17 (corrected item-total correlation: 0.050). Secondly, I think I should remove items that exhibit high inter-item correlations in the inter-item correlation matrix, particularly pairs that are close to 1 or -1. In these ways, I think I can get multiple correlation coefficient.

I hope you can provide further clarification and answer my doubt once again. Thank you for your assistance!

If you have highly correlated variables which could introduce multicollinearity. One way to resolve this is by estimating the VIF an removing variables with high VIF. 

Variance Inflation Factor (VIF): VIF measures how much the variance of an estimated regression coefficient increases if your predictors are correlated. High VIF values (usually above 5 or 10, depending on the context) indicate multicollinearity. Variables with high VIF values may need to be removed from the model.