We want to conduct exploratory analyses on the influence of personality (Big Five) on health trajectories in humanitarian aid workers. The health trajectories are unevenly distributed with a vast majority of staff being in the healthy trajectory. The internal consistency of the Big Five Inventory is fine and most personality traits correlate significantly with our health outcomes. Yet, the distributions of the personality traits are skewed and have a rather low standard deviation (e.g., agreeableness mean 4.15 out of 5 and SD 0.52). We were wondering if it statistically makes sense to enter these skewed and rather homogeneous data as a covariate in the growth mixture model. I cannot find any information on statistical requirements of covariates for GMMs. Does anyone have information on this or an advice? Thanks!
This paper delineates all the assumptions in GMMs pretty well,
Article Distributional Assumptions of Growth Mixture Models: Implica...
which states that "... it is assumed that the repeated measures are multinormally distributed, implying that the individual growth parameters and time-specific residuals are also multinormal".
There's a cool paper exploring problems using non-normal data in GMMs if you want more details too,
Article Growth Mixture Modeling: A Method for Identifying Difference...
It should not be a problem to add these covariates to your GMM. You can use robust estimation methods that take into account non-normality. A more severe issue may be the low variability (high homogeneity) in the covariates, which may prevent you from finding relevant covariate effects on class membership. But I would just try it out!
Thanks! I think the assumptions in Marius' refer to the repeated measure that we build the trajectories for, not the covariates? But for them, maybe this part from the assumption list is most important: "Finally, when predictors are included, it is standard to assume that their effects are constant over the range of the trajectory parameter values (e.g., that the effects do not differ for individuals with low and high intercepts)", which would be the case for our study
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