we used both information criteria and the bootstrap likelihood ratio test (BLRT) (McLachlan and Peel 2004). The Akaike information criterion (AIC) (Akaike 1987) and Bayesian information criterion (BIC) (Schwarz 1978) penalize the complexity of models (i.e. the number of parameters estimated), and lower values are preferred because they represent a balance between model fit and parsimony. The BLRT tests the difference of log likelihoods between models with k and k-1 class(es), and insignificant p-values indicate that a model with k classes fits no better than a model with k-1 classes.
