If you use TYPE=BASIC; and ask for H1SE; in the OUTPUT command, you can get standard errors for the means and covariances. If you need them for the correlations, you need to specify the means, variances, and covariances in the MODEL command, label the parameters, and use MODEL CONSTRAINT to define correlations. Mplus will then give standard errors for the correlations.
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I was wondering if I could use FIML estimation to estimate a bunch of correlations simply by using the WITH statement. However, the correlation estimates that I get from this procedure are completely different from those obtained by using TYPE=BASIC. In fact, when using the WITH statement I get an error which includes the text, "NON-POSITIVE DEFINITE FIRST-ORDER DERIVATIVE PRODUCT MATRIX ... PROBLEM INVOLVING THE FOLLOWING PARAMETER: Parameter 25"; when I look up this parameter via TECH1 output it is a totally implausible value (an extremely high covariance; the variance for one of the variables involved in this covariance is also extremely high, far outside plausible bounds). In general, the TYPE=BASIC correlations make much more sense given what we would expect from our data.
Is there any reason results obtained using the WITH statement would be so discrepant from those obtained with TYPE=BASIC? Syntax I used for the WITH statement is below. Many thanks.