I am currently conducting latent profile analyses in Mplus, but I have a hard time finding any recommendation for how to choose variance/covariance matrix. In my experience, less constrained models (with class-varying variances and covariances between items within classes) results in better fit statistics, but it is more difficult to find the "best" model (i.e., replicate the best loglikelihood values) and computing times increase substantially.
My current approach is to run a number of different specifications for variance/covariances and determine the best number of classes for each specification. Then I compare solutions for different specifications to see which solution that provides most relevant information about my study sample. But is there a more systematic approach to choosing variance/covariance matrix? Are choices based on a priori assumptions recommended? Are there any publications describing how to choose specification, e.g., for different types of data? Any help would be much appreciated.
You can take a look at the following paper that just came out:
Johnson, S. (2021). Latent profile transition analyses and growth mixture models: A very non-technical guide for researchers in child and adolescent development. New Directions in Child and Adolescent Development, 175, 111-139.
https://onlinelibrary.wiley.com/toc/15348687/current
Also, the following paper provides useful information regarding these issues:
Pastor, D. A., Barron, K. E., Miller, B. J., Davis, S. L. (2007). A latent profile analysis of college students’ achievement goal orientation. Contemporary Educational Psychology, 32, 8-47.
Article A latent profile analysis of college students’ achievement g...
Hey Anders
I suppose that Mplus has to choose a default model for LPA, and as far as I can remember it constrains the variability to be equal across classes for each indicator. Of course the model could be made simpler by adding further restrictions or more complicated by removing restrictions. Each of these actions will have an effect on the estimation of your model, put simply, improper solutions and convergence failures will tend to occur more often for models with fewer constraints.
This has been an issue in growth mixture models as it appears that certain specifications will result in particular attributes of the fitted model, such as larger or smaller 'baseline' classes. There is interesting simulation work...
Thierno M. O. Diallo, Alexandre J. S. Morin & HuiZhong Lu (2016) Impact of Misspecifications of the Latent Variance–Covariance and Residual Matrices on the Class Enumeration Accuracy of Growth Mixture Models, Structural Equation Modeling: A Multidisciplinary Journal, 23:4, 507-531, DOI: 10.1080/10705511.2016.1169188
..and more applied research
Infurna, F. J., & Luthar, S. S. (2016). Resilience to Major Life Stressors Is Not as Common as Thought. Perspectives on Psychological Science, 11(2), 175–194. https://doi.org/10.1177/1745691615621271
Unfortunately I don't have a direct answer to your question.
Mark
Christian Geiser and Mark Shevlin, thank you both for the references. I really appreciated the "non-technical" approach of the Johnson paper. It seems like the procedure I use is more or less the same as that of others, and there is no easy way of determining the best specification (although a less constrained model is better at reproducing the true class number, with the downside of resulting in more inadmissable solutions and longer computation times).
Mark Shevlin, yes that is correct, the default model for LPA in Mplus constrains the variance to be equal across classes, though they are allowed to vary within classes, and covariances are constrained to 0. This is the most constrained model I have used. I noticed that the references you provided mainly concern modelling with repeated measures, but I assume that certain conclusions would apply to the simpler LPA-model too. E.g., that the more restrained models have a tendency to over-extract classes, and that the least constrained model that converges without problem most likely represents the data best.