I am running a 3 class 13 wave quadratic growth mixture model and have two questions.
1) The model converged and terminated normally, however, the variance estimate for intercepts for the 1st and 3rd classes were negative. This seems to indicate some problems with the model, what are your suggestions (this doesn't happen in the linear model, only in the quadratic)?
2) The standard errors for some of the estimates are quite large for the quadratic 3 class model (e.g., class 2 the variance and mean of the intercept). What might be the problem? Again this is not the case with the linear model.
Thanks in advance. Moncia Oxford
bmuthen posted on Wednesday, November 29, 2000 - 4:03 pm
The fact that growth mixture modeling has more than one class tends to reduce the within-class variation and in some cases it can be set at zero. You may not get a significant worsening of fit (e.g by likelihood-ratio chi-square difference testing) if you fix the negative variance estimates at zero. If you do get a significant worsening of fit, this could indicate that the model is not appropriate for the data.
If you have class-specific parameters, standard errors could be large due to small class sizes.
The fact that your quadratic model seems to have more problems than the linear might point to the fact that you might only need a linear model once you allow several classes. A good way to vizualize your model-data fit on an individual level is mentioned in the growth mixture modeling paper number 87 as listed on this web site.
Thanks for the above response. I have one more question on the same model. I would like to add a time varying covariate, but, from what I understand, I can't run such a model with the current version of MPLUS, will this be a feature of version 2?
Unless I am misunderstanding you, there is no reason that you cannot have time-varying covariates as part of your growth mixture model. They would be specified as y1 ON x1 and y2 ON x2, for example. Example 22.1c in the Mplus User's Guide contains time-varying and time-invariant covariates in a growth model.
Hemant Kher posted on Wednesday, October 27, 2010 - 8:30 pm
Hello Drs. Muthen and Muthen,
I have a some questions on latent classes in a LGM. My sample has n=230 respondents. I have taken 4 repeated measurements on a continuous variable and fit a non-linear LGM.
1) The LRT test (tech11 output) shows that 2-class solution is significantly different from the 1 class solution. But, the two groups are quite apart in their sizes – 228 in one and only 2 in the other. In my readings I have not come across such a wide range and wonder about my results. The slope for the group with 2 students is almost 3.5 times that for the rest of the group, so I do see why the groups may be different.
2) The LRT test shows that 3-class solution is significantly different from the 2 class solution, but, now the residual variance for time point 4 measure is negative (p=0.8). Can I set this to zero given that it is not significant?
3) Setting the negative residual variance for time point 4 to zero results in a 3-class model with LRT that is significantly different from the 2-class solution – can I assume that this comparison is against a 2-class model where residual variance for time point 4 measure was also set to zero?
4) The LRT test shows that a 4-class solution is not different from the 3-class solution (p=0.0545). Can I conclude that my data contains 3 classes on the basis of these results?
Thank you so much for your time; it is greatly appreciated.
First, are you sure you are using enough starts? For example, try
Starts = 400 100;
Particularly with smallish sample sizes the mixture likelihood can be bumpy and in need of many starts.
Do a first quick scan of the number of classes using BIC. I would not choose a solution with only 2 students in it. But, if those two students are so different, I would delete them and then do the GMM - they may obscure other interesting mixtures.
The negative residual variance may point to the wrong functional form for the growth model - or that an outcome is very non-normal (floor or ceiling effect).
The R-square for the outcome at the first time point is the variance explained in that outcome by the growth factors. I think by first class intercept and slope, you mean the intercept and slope growth factors. R-square for these is the variance explained by the covariates they are regressed on.
See the Topic 3 course handout on the website around Slide 70. There is a path diagram of a conditional growth model that will make this clearer.