I am using the option TYPE = COMPLEX and the following warning message appears in Mplus version 4.1:
THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NON-POSITIVE DEFINITE FIRST-ORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS -0.476D-16. PROBLEM INVOLVING PARAMETER 48.
THIS IS MOST LIKELY DUE TO HAVING MORE PARAMETERS THAN THE NUMBER OF CLUSTERS.
It is true that in the model, there are more parameters than clusters. However, for exactly the same model no such message was output in Mplus 3.0 and 4.0. So I wonder whether one should be concerned about this? Do you recommend another option to correct for non-independence in cases where n(clusters) < n(parameters)?
This message has been in Mplus for a long time so I am surprised you didn't get it in Version 3. This is a warning. Your standard errors are most likely fine. The only way to know for certain would be to do a simulation study. It is probably most serious if you have more between parameters than clusters.
I tried running a ML path model, but the model was unable to converge, likely due to number of clusters and sample size within cluster. Alternatively, I ran TYPE = COMPLEX. In the path model, individual level variables are used to predict L2 variables. For this to happen, is Mplus aggregating the individual level predictors for each supervisor and using the mean predictor per supervisor to predict the L2 outcome, which is a supervisor level variable?
The fit of the model is acceptable and no errors were encountered. Your clarification is appreciated.
In type=twolevel analysis, variables that are observed for individuals and used on the between level (cluster level, level 2) are formed as latent variable constructs that are more reliable than cluster averages. We have a note describing this that we can send you if you send me an email. In type=complex, this is not done, but the users has to provide the cluster-level variables.
To diagnose the nonconvergence, you have to contact support.
I have 74 plots each with four sublots of decreasing size (imagine dartboards), so that my total sample size is 296. The size of these subplots is the exogenous variable for my SEM. I have used TYPE=COMPLEX to correct for non-independence in the endogenous variables due to clustering of subplots within plots. I am not interested in differences between the 74 plots (or sites), but in differences among the subplots across all plots. I thought this was a valid approach but one of my professors reviewing my work is skeptical. He thinks I should have had 296 indpendent plots of varying size, but I needed to cluster them due to practical concerns.
Can you provide a reference explaining how the TYPE=COMPLEX method adjusts SEs and the Chi-square so that we can work out whether my analysis is valid? Thanks for your help.