= 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.
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