When I Try to Run My Structural Analysis, I Get an Error Message About My Matrix Not Being Positive Definite

You will get this message when you have a negative eigenvalue in your matrix. A non-positive matrix is often the result of multicollinearity. For instance, let’s say you are examining the eating habits of children and you have two variables of “child height” and “child weight”. The linear correlation between these two constructs might be nearly perfect and the covariance matrix would not be positive definite.You can also get a non-positive matrix with a small sam- ple size simply due to sampling fluctuation. Lastly, you could also get a non-positive matrix if you have large amounts of missing data. With a simple mean replacement (which I don’t recommend), this might be the cause of the non-positive matrix.To see if this is the problem, try another method of data replacement. More than likely, a non-positive matrix is multicol- linearity between two constructs. If the problem is multicollinearity, you will need to remove covariances of error terms or, in the worst-case scenario, remove a structural relationship between the two highly correlated variables. Ultimately, you might even need to drop one of the problematic variables from the model if the issue persists.

Source: Thakkar, J.J. (2020). “Procedural Steps in Structural Equation Modelling”. In: Structural Equation Modelling. Studies in Systems, Decision and Control, vol 285. Springer, Singapore.