1) If I have a multi-class model, but don't specify any particular model for the mixture (i.e., classes are not regressed onto any variables, no variables are regressed onto classes, and nothing is specified as varying across classes), then what does the model mean? How are the classes derived?
2) I see that in Ex 10.2 the within-groups latent variable is shown as being regressed onto a latent class factor, but this is not explicated in the "model" command. By specifying multiple classes in a m-level model, does this automatically regress a within-groups variable onto a latent class variable?
3) How different is a model that specifies different means for a variable across classes and a model which regresses the same variable onto a latent class variable? Either way, the model specifies that average levels of the value will vary across classes, correct?
4) Finally, if I have, for example, a 4-class model and only specify a relationship for the first class (e.g., Y1 ON C#1), then how are the remaining classes specified? In other words, with more than two classes, but only explicating some relation for the first class, how does the model determine the other classes?
Thanks for help with these problems!
bmuthen posted on Thursday, August 25, 2005 - 8:45 pm
1. The default is to let observed variable means or threshold vary across classes. So like in LCA where classes are defined by differing in their item (mean) profiles while having the variables uncorrelated within classes.
2. The picture for ex10.2 has a symbolic arrow from c to fw. As in LCA, the influence of c on another variable implies by default in Mplus that the mean (or threshold) of that other variable varies across the classes of c - the analogy is regression onto a dummy variable; conceptually this is what is done.
3. Mplus does not allow you to say "fw on c", but conceptually this is what is done.
4. Following from above, Mplus does not allow "y1 on c#1" except on the between level where c#1 is a continuous random intercept variable. If you don't have thew between statement say "y1 on c#2", this implies that only the random intercept for c#1 influences y1.
Sorry, but if you could elaborate: Without specifying any particular relations for the latent classes (in, for example, a 3-class model), but with relationships specified for other variables in a model, then how will the classes be determined. Will the model classify within or between variance; will the model classify DVs or IVs?
E.g., (with 3 classes)
%WITHIN% %OVERALL% y1 ON x1 x2;
%BETWEEN% %OVERALL% y1 ON x1 x2;
Which part of the model's variance is used in class formation? And, if you have (1) more than one DV and/or (2) a random slope, would it operate in the same way?
bmuthen posted on Thursday, August 25, 2005 - 9:49 pm
For 2-level models, the latent classes are determined by within-level information, i.e. the latent class variable is a within-level variable. So in your case, this means that classification is based on information from within-level (co-) variation for your y1, x1, and x2 variables. You have a regression mixture model, where the regression also has a random slope (called "y1" on the between level) which is regressed on between-level variation of x1, x2.
1) for a model where heterogeneity at the within-groups level is classified, and the same class variable is employed at the between-groups level, how does classification function? For example: with 4 people in two groups (2 people per group) and a class variable that (correctly) recognizes that one person from each group should be in a class 1 and one person from each group should be in a class 2, how can the class variable be used at the between-groups level at all? Any attempt to classify groups using the same class variable would seem to force the class variable to both contain and not contain the same people, because their group-membership would conflict with their class membership. Does this question make sense?
2) with mixture modeling, comparing models with the same number of classes but with different model constraints (e.g., with vs. without equal factor loadings), is it correct that (-2) log-likelihood difference tests may be conducted? Lubke & Muthen, 2005 seems to suggest this, but doesn't say it explicitly.
BMuthen posted on Monday, September 05, 2005 - 8:37 pm
1. It is not the class variable that is used on the between level but a random intercept of the class variable which is a continuous variable varying across the between clusters. I hope that answers the questions.