One of the great features of Mplus 3 is the possibility to specify non-linear constraints. This approach works well in the traditional SEM framework where no data-clustering is assumed. However, I have made the experience that the inclusion of non-linear constraints in conjunction with the ‘complex data’ option reveals the wrong / uncorrected test statistics. The fit indices are equivalent to the ML results when no clustering is assumed. This problem seems not to be specific to the data I use. Equivalent models (with and without non-linear constraints) revealed different fit indices when using the ‘complex’ option. When using the non-linear constraints the model-fit was exactly the same for ‘type = general’ and ‘type = complex’,respectively. This was not true for the unconstrained model. What can I do to get the correct fit statistics for models that include non-linear constraints in a situation where the data is clustered?
bmuthen posted on Wednesday, September 01, 2004 - 5:11 pm
Gabriel posted on Thursday, September 02, 2004 - 5:26 pm
Thanks for the offer, but I first have to ask my boss... However, I think that the problem involves mainly situations where latent variances are constrained. The ‘complex’ procedure does not work in situations involving direct estimates of standardized paths. An example is a regression between two standardized latent variables with both total variances fixed to 1. This procedure works well when the variance of the predictor variable is fixed to 1 and the residual of the dependent variable is constrained to be 1 – b**2. This kind of model works in the general modeling framework. The fit is equivalent to a model with reference loadings fixed to a value of 1 and freely estimated variances. However, when I fit the constrained model using the complex option, I always get a scaling correction factor of 1. This is not the case when I use the ‘traditional’ model specification. Maybe I’m wrong, but my understanding is that both models are (or should be) equivalent and therefore the fit statistics / correction factors should be equivalent as well. Thanks Gabriel
bmuthen posted on Friday, September 03, 2004 - 2:48 pm
Perhaps you can send at least the output so we can help you.