Our analysis comprised three steps (see Supplementary Figure 1): data reduction, cluster analysis, and heritability estimation. First, we used variable selection (Guyon and Elisseeff, 2003) and multiple correspondence analysis (MCA) (Abdi and Valentin, 2007; LeRoux and Rouanet, 2009; Murtagh, 2007) to reduce the large number of variables. In the variable selection step, we focused on the selection of withdrawal signs and symptoms, which was the largest subset of variables in the analysis. The MCA data reduction approach is similar to principal components analysis but it compacts categorical (rather than continuous) data to a lower-dimensional space (Greenacre and Hastie, 1987). The retained principal dimensions are those that explain substantial variance in the data. The output of MCA comprised the coordinates of the retained dimensions for each of the 5,390 subjects. MCA was first used to find the principal dimensions for the 15 “occur together” symptoms and the 15 “ever occur” symptoms, respectively. The variability and heritability of these two sets of principal dimensions were compared to select between the two sets of variables. MCA was then applied to all of the
