A multivariate generalized linear mixed model (GLMM) with probit link was used24. The probability P for an individual having a disease is determined by a latent risk variable R, corresponding to the area under the standard normal curve – i.e., a small value of R indicates a small probability. Our model specifies R as the sum of several effects, including family-member type (father, mother or children), additive genetic (Asz, Abp), adult shared environmental (Fsz, Fbp) and childhood shared environment (Csz, Cbp) effects along with a common non-shared environmental effect for both schizophrenia and bipolar disorder (E). For schizophrenia and bipolar disorder, our models are Fsz = βszfIf + βszmIm + βszcIc + Asz + Fsz + Csz + ERbp = βbpfIf + βbpmIm + βbpcIc + Abp + Fbp + Cbp + E where If, Im and Ic are indicator variables for father, mother and children, βf, βm and βc are fixed parameters associated with disease prevalence for respective family members. The random effects A, F, C, and E are assumed to be normally distributed with mean zero and a
