assumption results in a different number of classes, we tried to fit LPA models with skewed t-distribution. However, estimating this model was extremely slow, likely due to the large number of SNPs, and the model never converged. On the other hand, clusters from k-means clustering, which does not assume conditional normality, had comparable profiles and proportions to LPA results. Although the sphericity assumption of k-means, which assumes the same within-cluster variance, may also not be appropriate for the distance metric used our analysis, −log10(p-values), the consistency of results from methods that require different sets of assumptions may indicate that classes identified in LPA are robust to the violations of assumptions. As pointed in Muthén (2003), the interpretation of classes identified from latent categorical variable models is rather a substantive question, and incorporating substantive knowledge is an important step to validate identified classes. Consistency of classes identified in our study with the expectation based on twin studies provides a theoretical support in interpreting identified classes. Further investigation of identified classes utilizing auxiliary information, such as predicting class membership by covariates or using class memberships to predict distal outcomes, would be important step to validate classification results.
