When you have NOMINAL indicators, for example, your model gives rise to expected counts that can be compared to observed counts. The distribution theory is based on the chi-square statistic (L-squared), which has an associated p-value. When you have CONTINUOUS indicators, your model is based on normal theory. The parameters being estimated are means, variances, and covariances. Since the data are continuous and not discrete, you no longer have a model framework of observed and expected counts. The model is the normal finite mixture model. Classification can work well with a good-fitting model.
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