I am analyzing data using mixture modeling. When I plot the information criteria (the BIC) for a series of models (with different model specifications and different number of mixture components), I notice a very steep decrease in the BIC. E.g., in the photo below, the fitted model represented by the grey lines (and points) with five profiles (or components) has a much lower BIC than that with four components (the BIC decreases by around 50%). Similar for the model represented by the red line between five and six mixture components.
Is this a cause for concern? Or is it likely that this is due to real improvements in the model fit when an additional component is added? It seems like a change of this magnitude, all other things being equal, is cause for concern. What would you to do to follow-up on this analysis to determine whether the change in the log-likelihood is spurious and problematic or indicative of (practically) meaningfully better fitted models?