At this moment I am running a multilevel model with a cross-level interaction using the MLR estimator. Above my model results I find the following warning:
MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS -1011.058
WARNING: THE MODEL ESTIMATION HAS REACHED A SADDLE POINT OR A POINT WHERE THE OBSERVED AND THE EXPECTED INFORMATION MATRICES DO NOT MATCH.AN ADJUSTMENT TO THE ESTIMATION OF THE INFORMATION MATRIX HAS BEEN MADE. THE CONDITION NUMBER IS -0.672D-03. THE PROBLEM MAY ALSO BE RESOLVED BY DECREASING THE VALUE OF THE MCONVERGENCE OR LOGCRITERION OPTIONS OR BY CHANGING THE STARTING VALUES OR BY USING THE MLF ESTIMATOR.
THE MODEL ESTIMATION TERMINATED NORMALLY
For me, this warning sounds like Mplus made an adjustment and that I can interpret my cross-level interaction. Is this correct? Or do I need to make an additional adjustment myself? The strange thing is that the cross-level interaction disappears when I change the estimator from MLR to MLF... Does this mean that the identified cross-level interaction is a statistical artefact?
I have also estimated a multilevel model to estimate a cross-level interaction and obtain a similar error message. I have two questions: (1) When is it safe to "ignore" the warning ? When it says that the model estimation terminated normally? And (2) how would you report this in an article? That an adjustment to the information matrix has been made and then make a reference to the article by Tihomir and Bengt on the issue http://www.statmodel.com/download/SaddlePoints2.pdf ? Or not mention it at all since the model estimated normally?
My warning message is this:
WARNING: THE MODEL ESTIMATION HAS REACHED A SADDLE POINT OR A POINT WHERE THE OBSERVED AND THE EXPECTED INFORMATION MATRICES DO NOT MATCH. AN ADJUSTMENT TO THE ESTIMATION OF THE INFORMATION MATRIX HAS BEEN MADE. THE CONDITION NUMBER IS -0.998D-03. THE PROBLEM MAY ALSO BE RESOLVED BY DECREASING THE VALUE OF THE MCONVERGENCE OR LOGCRITERION OPTIONS OR BY CHANGING THE STARTING VALUES OR BY USING THE MLF ESTIMATOR.
(1) I think it is typically safe to ignore the warning; it is mainly given as information about which SE estimator is used. If you can eliminate reasons 1. and 2. mentioned in the tech note that you refer to, then you should be fine.
(2) I would report that the SEs are computed with this method, giving a reference to the tech note.
I estimated a multilevel model with cross-level interactions. I used integration = montecarlo and mconvergence = .01, MLR, and ADAPTIVE = off; I obtained the WARNING: THE MODEL ESTIMATION HAS REACHED A SADDLE POINT message. Based on recommendations in the tech report about saddle points, I reran the model with 500 integration points (I read this is normally the standard; the original model where I made no specifications on number of integration points had 326) and mconvergence = .001. I also included STARTS 150 15; the message did not go away. At that point, I upped to 5000 integration points given the manual states this is a good idea if you have more than 3 dimensions (I have 4). Still get the message. Dr. Bengt Muthen notes above that the Saddle point warning can be ignored as it generally only affects SE estimation but I noticed that in the models with more integration points and the smaller convergence value, the effects of the cross level interactions were no longer significant (one was in the original model) and the level 2 parameter estimates all diminished slightly (including my level 2 main effect, which is .083 and significant(p=.046) in the original model, .079 (p=.056) in the 500 integration model, and .077 (p= .142) in 5000 integration point model. I am worried- does this suggest the results I found with fewer integration points and larger mconvergence are not trustworthy?
The more integration points and the sharper convergence criterion, the more precise the logL, estimates, and SEs. You have do do trial and error. You can even use the default integ=15, which with 4 dimensions gives 50625 integration points, that is, many more than the 5000 of Monte Carlo integration. It will be slower, however. Generally speaking, I don't think you want to have as lax of a convergence criterion as mconv =0.01.