I am using the MCLUST software in
R to fit normal mixture models, as part of what in my field are commonly called Latent Profile Analysis.
Some of the time, models do not converge, and an error to indicate as much is returned in lieu of output. Other times, the model appears to converge, but some (one or more) profiles / mixture components are without any observations classified to them. This apparently is because the posterior probabilities for any profiles without any observations classified to them are less than the posterior probability for another model. MCLUST, for its part, outputs a warning and I am curious as to why it is not an error (or a more strongly-worded warning!).
In such cases, how should such models be interpreted? Should they be rejected - considered non-interpretable? Are there cases where a model that converges but which has a profile / mixture component without any observations classified to it still contains useful information on its own or in relation to other models?