

Weight Matrix Not Positive Definite 

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Hi, I am running CFAs with categorical variables and I came across a problem. When the models are estimated with WLSMV, I get proper solutions. If, however, I use the WLS to estimate the same models, I get a fatal error message indicating that "the weight matrix is not positive definite as it should be". My questions are: 1) Why is the matix poisitve definite in one and not the other? Can the problem be fixed? 2) What other estimator can I use to compare model fit indices (if I cannot use WLS)? Thanks for your help.  Mesfin 

bmuthen posted on Tuesday, September 10, 2002  8:46 am



The message means that the full weight matrix is not positive definite which it should be when the necessary inversion of the matrix takes place for WLS. WLSMV uses only the diagonal of this matrix and therefore does not run into this problem. The nonpos definiteness is typically due to too small of a sample relative to the skewness of the items. To compare models you would then instead have to rely on comparing fit indices such as CFI and WRMR descriptively, since no statistical difference test is available for them. Alternatively, skewed items would have to be removed. Or if possible, the sample size has to be increased, e.g. by not considering subgroups but the full sample. 

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