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Hi, I am interested in comparing a 3 class SEM with a 4 class SEM. However I noticed that the measurement model parameters vary across these two models unless I estimate them in a separate measurement model and hold them fixed across these two models. Currently I am fixing the loadings and the residual variances of the items. Shoudl I also fix the variances of the exogenous factors to measurement model values? 


When you go from 3 to 4 classes, I think you would expect the parameters to change because some observations from the three classes are leaving those classes and moving to a fourth class. I would not fix any parameters. 


Hi Linda, I want the observations to be classified only based on the structural regression coefficients and not on the measurement model parameters. If that is the case can I fix them? Thanks 

bmuthen posted on Wednesday, February 15, 2006  8:27 am



It sounds as if you hypothesize that your measurement parameters are invariant across classes. If so, these parameters can be held equal across classes, letting only the structural parameters differ across classes. However, even if you do this, your measurement parameters will have different estimates in the 3class analysis and the 4class analysis. To me, that is how it should be because you are applying different models. I may not understand the features of this particular application that would cause you to take that approach, but it sees strange to me to use estimates of measurement parameters from a 3class analysis as fixed values for measurement parameters in a 4class analysis  these fixed values may be far away from the best maximumlikelihood estimates that you would obtain if these parameters were freely estimated in the 4class analysis. 


Hi Linda, Thanks for your comment. I want my classes to arise only due to the strutural regression coefficients. I was trying to figure out a way to compare models on an even basis following suggestions by Anderson and Gerbing 1988's two step estimation of SEM models (measurement and structural parts to be estimated separately) and the Steenkamp and Baumgartner 1998 article on measurement invariance. I really appreciate your comments. Also, it would be very nice if Mplus allows more flexibility in constraining parameters to be positive only. I need to constrain 10 parameters in my model to be positive in their estimates (based on hypotheses), the trick that you discussed in the message board sets the parameter at a certain value. It would be nice if instead of setting it at a value, one could just say that it is >= 0 . 

bmuthen posted on Thursday, February 16, 2006  6:19 am



Letting classes arise due to only structural regression coefficient differences will be accomplished when holding measurement parameters equal across classes. But, that may not be the bestfitting model  but you can check. The upcoming version 4 of Mplus has the parameter constraint feature that you ask for. 


Thanks Dr. Muthen, that would be a welcome feature. 

Andy Ross posted on Friday, November 21, 2008  4:34 am



Dear Prof. Muthen Is it possible to use BIC to compare two simple latent class models which are the same except for the configuration of the indicator variables. For example, a latent class model that uses 3 categorical indicators and 1 continuous indicator to be compared with a model which for all sense and purposes is the same, except the continuous indicator has been been transformed into a categorical indicator (i.e indicating quartiles of the original measure)? Many Thanks Andy 


The BIC scale would not be the same in these two cases so BIC cannot be used to compare these models. 


Greetings, This question may potentially appears stupid. Sorry for that. When we compare mixture models with a similar number of classes, those models can be compared with likelihood ratio tests (not applicable for the comparison of models with different number of classes). In this case, are the observed loglikelihoods directly comparable or is it necessary to take into account the scaling factors (the default estimator for mixture models beeing MLR). I'm asking since Mplus does not print any warnings on this subject (as it does for classical SEM and CFA models) estimated with MLR. Also, I did play with some models and found out that MLR and ML estimates of mixture models usually converge on identical loglikelihoods (but different errors estimates, which is normal), but models comparisons do not converge on similar conclusions when scaling factors are taken into account. In summary: Do you recommend the use of the scaling factors in model comparions (MLR mixture estimation). Thanks in advance. 


I would always recommend using the scaling factor. The MLR estimator is a safeguard against heteroscedasticity, nonnormality and complex sampling design effects. Using the MLR scaling factor will carry these safeguards even in the LRT testing. The LRT testing with the MLR estimator is described at http://statmodel.com/chidiff.shtml 


As a follow up on my previous question, In mixture models, it is possible to compare nested models, meaning models with the same variables and the same number of classes, with classical likelihood ratio tests (e.g. to compare a 3class LCGA, with a 3class varianceinvariant GMM, and with a 3class variancevarying GMM). Will the same be possible if I wish to compare models (lets say GMM, all with the same variables and the same number of classes) in which: (model 1) I predict class membership from X predictors; (model 2) Model 1 + the predictors are also used to predict the intercept and slope factor; (model 3) Model 1 + the predictors are also used to predict the intercept, slope and quadratic factor; (model 4) Model 3 + the “isq on predictors” regression vary across classes; (model 5) Model 3 + the predictors also predict a distal outcome (which is already in models 14). In other words, are these models nested ? 


Yes. Yes on all. 


Thanks, I just wanted to make sure. It seemed logical but I never saw it used in conditional model comparisons (and never saw anyone take the scaling factor into account in any kind of Mixture models comparisons). 

fred posted on Saturday, November 04, 2017  10:28 am



Dear all, in comapring two nested models in a mixture model with knownclasses and based on difference test based on loglikelihood values and scaling correction factors , I am using the formula "TRd = 2*(L0  L1)/cd" Since DF is calculated by the difference between the number of parameters, I assume that if the test is nonsignificant the model with lower number of parameter (highest DF) is to be prefered. Is this a correct interpretation of the function of the number of parameters given in mixture model output? 


That's correct. 

fred posted on Saturday, November 04, 2017  4:45 pm



Thank you very much Bengt. Perhaps you could explain a pattern in the output that is less than clear to me. I am trying to assess a moderation (or rather a moderated mediation). First by letting one structural path between predictor and moderator freely estimated I get a nonsignficant scaled chi squre value, which then I interpret as keeping the constrained model, i.e. no moderation. But the path in one of the group is highly signficant and in the other group it is nonsignficant, isn't this indication of moderation, and how can the nonsignficant chi2 value be explained then? Also is there a way to test the parameter equality across the classes directly in the mixture model , similar to difftest? 


These general analysis questions are suitable for SEMNET. In mixture models, Model Test can be used to test parameter constraints. 

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