Troubleshooting
Problem
I want to run a factor analysis in SPSS for Windows. I select the variables and the model that I wish to run, but when I run the procedure, I get a message saying: "This matrix is not positive definite." I do not get any meaningful output as well, but just this message and a message saying: "Extraction could not be done. The extraction is skipped." Why is this happening?
Resolving The Problem
The error indicates that your correlation matrix is nonpositive definite (NPD), i.e., that some of the eigenvalues of your correlation matrix are not positive numbers. If you request a factor extraction method other than principal components (PC) or unweighted least squares (ULS), an NPD matrix will cause the procedure to stop without extracting factors. If one or more of the eigenvalues are negative, then PC and ULS extraction will also terminate.
Matrices can be NPD as a result of various other properties. A correlation matrix will be NPD if there are linear dependencies among the variables, as reflected by one or more eigenvalues of 0. For example, if variable X12 can be reproduced by a weighted sum of variables X5, X7, and X10, then there is a linear dependency among those variables and the correlation matrix that includes them will be NPD. If there are more variables in the analysis than there are cases, then the correlation matrix will have linear dependencies and be NPD. Remember that FACTOR uses listwise deletion of cases with missing data by default. If you had more cases in the file than variables in the analysis, listwise deletion could leave you with more variables than retained cases. Pairwise deletion of missing data can also lead to NPD matrices. Negative eigenvalues may be present in these situations. See the following chapter for a helpful discussion and illustration of how this can happen.
Wothke, W. (1993) Nonpositive definite matrices in structural modeling. In K.A. Bollen & J.S. Long (Eds.), Testing Structural Equation Models. Newbury Park NJ: Sage. (Chap. 11, pp. 256-293).
Wothke's chapter also provides some suggestions for diagnosing NPD matrices, including the use of principal components analysis to detect linear dependencies.
Related Information
Historical Number
24433
Was this topic helpful?
Document Information
Modified date:
16 April 2020
UID
swg21477275