Nonregular mixture model selection

Testing the number of components in a finite mixture model is nonregular: absent components have zero weights on the parameter boundary and their means or other parameters are unidentified. The usual chi-squared limit for a likelihood-ratio test therefore need not apply. Information criteria are useful working comparisons, while parametric bootstrap and predictive cross-validation can provide more appropriate evidence. Neither a mixture fit nor a selected component count proves genuine latent populations.