We use lfmm gibs sampler model to generate logit(P_ij) then we generate binary data G_ij
1 2 3 | lfmm_logit_sample(n, L, K, outlier_prop = 0, gamma = 1, gamma_mu = 1,
gamma_U = 1, gamma_V = 1, gamma_B = 1, mean_B_outlier = 0.5,
cor_U1_X = 0.5)
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