I got an error message from the analysis of multilevel data. There are several errors reported.
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 -0.143D-16. PROBLEM INVOLVING PARAMETER 215.
THE NONIDENTIFICATION IS MOST LIKELY DUE TO HAVING MORE PARAMETERS THAN THE NUMBER OF CLUSTERS. REDUCE THE NUMBER OF PARAMETERS.
THE MODEL ESTIMATION TERMINATED NORMALLY
THE H1 MODEL ESTIMATION DID NOT CONVERGE. SAMPLE STATISTICS COULD NOT BE COMPUTED. INCREASE THE NUMBER OF H1ITERATIONS.
I would like to know if the non-positive definite first-order derivative product matrix is the one identified as parameter 215.
Another problem is the model is unidentified due to the number of parameters over that of clusters. I can't reduce number of parameters. I remember you once suggested an analysis using Monte Carlo. Could you please suggest how to start.
Lastly, could you please advise how to increase the number H1 iteration as suggested by the system.
The entire matrix is non-positive definite. It is because of parameter 215.
You can set up a Monte Carlo study using the sample size and parameter estimates from your study including the number of clusters. Then you can see if you can recover the parameter estimates and standard errors given that you have more parameters than clusters.
I tried to set up the Monte Carlo simulation for my study as suggested. I think I can follow the guideline provided in Example 12.11. I am however stuck by the term NCSIZES, CSIZES and NREP. I have the following details for my data analysis:
Type = TWOLEVEL Number of Cluster = 213 Number of free parameters = 240 Observations = 1481
I think my NCSIZES is 213 but I don't understand how to identify the values for CSIZES and NREP.
NCSIZES specifies the number of unique cluster sizes. So if all clusters had ten observations, NCSIZES = 1, that is all clusters have the same size. CSIZES specifies the number of clusters and their sizes. CSIZES = 100 (100; says there are a hundred clusters and they are all size 10. See these options in the user's guide for further information.
The NREP option tells the number of replications you want in your simulation.