where γ1 denotes the effect of the first axis. We perform a likelihood ratio test of association, γ1 = 0, and retain the effect in the model if P<0.05. We then proceed in a forward selection manner, testing for association of each axis of genetic variation, xt, in turn, in order of decreasing eigenvalue, retaining any effect in the model for which P <0.05. We define an indicator variable zt, taking the value 1 if the tth axis of variation is associated with disease (P <0.05) and 0 otherwise. In the absence of population structure, we would expect no axes of genetic variation to be retained in the model, and hence zt = 0 for all t.
