We then made the assumption that the latent variables and electroencephalogram (EEG) variables are phenotypes that could be used to identify more homogeneous alcoholism phenotypes. We performed a canonical discriminant analysis using each of the latent variables as a potential grouping variable for the EEG variables. Although the p-values are not valid due to the non-independence of family members, they gave us an approximation of the relationships between the latent variables and the EEG variables. We found that latent variables 1 (persistent desire to stop drinking), 2 (morning drinking), 7 (gave up activities to drink), 9 (withdrawal symptoms), and 11 (emotional psychological problems from drinking) showed evidence of significant grouping with the EEG variables. Motivated by these observations, we defined ten derived phenotypes named Ai_j for i = 1, 2 and j = 1, 2, 7, 9, or 11 as defined above; an individual was affected with derived phenotype Ai_j if they were defined as alcoholic under definition 'i' and also had the symptom defined by latent variable 'j'. Correlations between these phenotypes were all higher than those between the
