Problem with multiple group CFA with censored variables using Mplus

I'm having problems running a multigroup CFA in Mplus for my dissertation, based on the established 4-factor model of the Hamilton Depression Scale (21 items). My dataset includes 4 left censored variables which I think may be the problem.

After the original CFA failed to output normally, I've rerun the analysis increasing the number of iterations, as advised by Mplus, but at Miterations = 2000 the output is stating;

THE LOGLIKELIHOOD DECREASED IN THE LAST EM ITERATION.  CHANGE YOUR
MODEL, STARTING VALUES AND/OR THE NUMBER OF INTEGRATION POINTS.

THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ERROR IN
THE COMPUTATION.  CHANGE YOUR MODEL AND/OR STARTING VALUES.


I have no idea what I can do next, any advice would be gratefully received.

When complicated things are going wrong, look to simple things :-).

Things to look at What does the correlation matrix look like? How severe is the left censoring? How different are your data from those in the FA you are trying to confirm?

Then you could try an exploratory FA, to see if your data have 4 factors (much less the same four).

Assuming that your model is correctly specified, then it looks like the likelihood is highly non linear or unreliable at neighborhood of the last iteration which seemed to be maxima (likely a local one). My strategy would be to try several starting values by using the STARTING option which allows you to set the number of starting value sets.

I suppose that your are not modeling the censoring. In that case your estimates risk to be biased but your model will stay numerically simpler (modeling the censorship may exacerbate your numerical issues). If you are modeling the censoring, it might be a good idea to pick up starting values from a simpler model, the one without censoring, and then rerun the complete model.