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1 year ago in Psychology , Statistical Analysis By Govind

When the observed correlation matrix is non-positive definite, under what conditions can factors still be extracted, and how does this affect the validity of the factor structure?

During my scale validation, the correlation matrix for my items became non-positive definite, often due to high multicollinearity or linear dependencies. I understand this is a problem for computation, but I’ve seen references that factor analysis can sometimes proceed. I need to know when it's technically possible to proceed and how it impacts the trustworthiness of the resulting factor structure.

 

ConceptMatrix Statistical Analysis

All Answers (1 Answers In All)

By Prajwal Sharma Answered 1 year ago

A non-positive definite (NPD) matrix is a serious red flag, indicating your variables are not linearly independent often from extreme multicollinearity or duplicate items. Technically, factor extraction can sometimes proceed if the negativity is confined to smaller eigenvalues ignored during extraction. However, in my experience with scale development, this is fraught. Even if you get a solution, it is often unstable, with unreliable variance estimates, and can lead to Heywood cases (communalities > 1.0). I would recommend you never ignore this. Diagnose the cause: remove redundant variables, combine highly correlated items, or increase your sample size. Proceeding without fixing the NPD matrix critically undermines the validity of your factor structure.

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