Structural Equation Modeling - Covariance Matrices vs. Correlation Matrices
In the Data to Analyze box of the Analysis Parameters dialog box, select which type of data to analyze. For standard path analyses or structural equation models, you choose either Covariances or Correlations. Use the following information to help you decide whether you should use the covariance or correlation matrix.
The Statistical distribution of the elements of a covariance matrix is not the same as that of a correlation matrix. This is obvious if you consider the diagonal elements of a covariance matrix, which are the variances of the variables. These are random variables - they vary from sample to sample. However, the diagonal elements of a correlation matrix are not random variables - they are always 1. The methods employed by previous structural modeling programs are based on the assumption that a covariance matrix is being analyzed. The sampling distribution theory they employ is not applicable to a correlation matrix, except in special circumstances.
Recent research has emphasized that it is possible (indeed likely) that you will get some wrong results if you analyze a correlation matrix as if it were a covariance matrix. However, a number of currently distributed structural modeling programs will analyze a correlation matrix as though it were a covariance matrix. The fact that such programs yield incorrect results has been described in the literature (see, for example, Cudeck, 1989). In order to provide compatibility with these other programs, SEPATH will analyze a correlation matrix as if it were a covariance matrix, but it can, unlike most other programs, directly and automatically provide correct analysis of a correlation matrix as well.