Simulation analysis: pair-wise scatterplots (for correlations) among the estimated means for clusters of the mixture model from simulated data. The mixture model assumes that there is no correlation among groups. These subfigures indicate that in our model, most of the means are not correlated to one another, which exactly obeys the assumptions; but some of them were weakly correlated. This may be due to outliers being treated as separate clusters. These clusters could have positive correlations that were not separable from other clusters. The Pearson correlation coefficients for pair-wise correlations (for clusters i vs. i+1, i = 1, 2,...,5) between two normal distributions were 0.0632, -0.0237, 0.1056, -0.0333, 0.0346, -0.0184, -0.0065, 0.0400, -0.0490, 0.0701, -0.0015, 0.3823, -0.4103, 0.3925, 0.3327, respectively.