The local independence assumption of LPA requires class indicators to be uncorrelated within each class. However, some indicators are moderately correlated within the classes identified in our analysis. We examined the within-class correlations between indicators based on most-likely class memberships from the 3-class model. The correlations between indicators in overall sample, ranged between 0.148 and 0.302, were reduced within each class, ranging between 0.009 and 0.219. However, some correlations, such as between AD and ASP (0.219) in the MD class and between MD and ASP (0.197) in the AD+ASP class, for example, remained substantial. This pattern of within-class correlation may indicate an extra source of correlations between the p-values other than the classes. LD structure may not likely be the cause because within-class correlations with the pruned (r2 = 0.1) set of SNPs showed similar patterns of within-class correlations to full set of SNPs. To incorporate common variance within classes, we fit the 3-class model with within-class residual covariance between indicators allowed. The result indicated no noticeable change in class proportions and profiles. Estimated residual correlations were substantial especially between
