In a GMM analysis, I am trying to decide whether to use a linear or a quadratic growth model, I am wondering if there are some guidelines for how to approach this. Shall I 1) fit a regular growth model(with 1-class) first, and decide to include the quadratic term or not (I assume using the chi-square test for nested model), and then fit the GMMs to decide the # of classes; or 2) decide the # of classes in GMM, and then decide if I should include quadratic terms? It's hard to know if each latent class would need the quadratic term though. Your guidance would be greatly appreciated!
Related to the above discussion, we have estimated an unconditional growth curve that demonstrates better fit with quadratic than linear model. As a next step we looked at a 5 class latent class growth model. In this model, the three most substantively interesting classes have non-significant quadratic means. Additonally, the slopes for these 3 classes are also non-significant, but eyeballing their graphs it would appear there is a significant slope. I'm wondering if the incorrect inclusion of a quadratic term for these 3 classes could be affecting the significance of the slope mean estimate? The two other classes, which have a higher N (ex.-stable low class) do however, demonstrate a significant quadratic mean.
In this case, do you suggest maintaining the same quadratic or linear model for all classes? Or is it possbile/correct to specify different models (linear vs quadratic) for the different classes? If this is the case, is there a reference you are aware of for how to go about settnig this up? Thanks so much