Corr matrix not positive definite

[kaodubela]

Hey!

I want to do a path analysis with proc CALIS but I keep getting an error that my correlation matrix is not positive definite. 

Is there a way to make the matrix positive definite? Its a 43 x 43 lower diagonal matrix I generated from Excel. I don't want to go about removing the variables one by one because there are many of them, and that will take much time too.

Thanks!

[Reeza]

How did you calculate the correlation matrix? I would recommend doing it in SAS so your full process is reproducible.

[kaodubela]

Thanks. I'll get the Corr matrix with SAS for a start.

[PaigeMiller]

A correlation matrix can fail "positive definite" if it has some variables (or linear combinations of variables) with a perfect +1 or -1 correlation with another variable (or another linear combination of variables).

In that case, you would want to identify these perfect correlations and remove at least one variable from the analysis, as it is not needed.

[kaodubela]

Thanks. I'll check the matrix for such variables. 

[pau13rown]

@Rick_SAShad a blog post about this: https://blogs.sas.com/content/iml/2012/11/28/computing-the-nearest-correlation-matrix.html

[Rick_SAS]

What does "Lower diagonal" mean?  A correlation matrix must be symmetric. If you don't have symmetry, you don't have a valid correlation matrix, so don't worry about positive definite until you've addressed the symmetry issue.