I am testing several CFA measurement models with Lavaan in R. The questionnaire that I am investigating has been shown to be composed of 1-factor, 3-factor, and 4-factor.
In the dataset, I found that the 1-factor and 3-factor fit okay, but the 3-factor fits best (lowest AIC).
However, the 4-factor model could not be tested because the "covariance matrix was not positive definite". A closer look revealed that one of the factors has an above one correlation with another factor.
My question is, why is it that the covariance matrix was not positive definite in the 4-factor model in my dataset? Is this problem unique to my dataset?
I am still a beginner, so I might miss some important details.
Thank you very much for the fast response everyone! Update: The sample is 904 participants and there are 28 observed variables (items) in the model.