code: def gen_simple_logit(nc, cs, s):
      np.random.seed(3799)
  
      exog_vc = np.kron(np.eye(nc), np.ones((cs, 1)))
      exog_fe = np.random.normal(size=(nc * cs, 2))
      vc = s * np.random.normal(size=nc)
      lp = np.dot(exog_fe, np.r_[1, -1]) + np.dot(exog_vc, vc)
      pr = 1 / (1 + np.exp(-lp))
      y = 1 * (np.random.uniform(size=nc * cs) < pr)
      ident = np.zeros(nc, dtype=int)
  
      return y, exog_fe, exog_vc, ident
  
imports: import numpy
  from statsmodels.genmod.bayes_mixed_glm import BinomialBayesMixedGLM, PoissonBayesMixedGLM
  import pandas
  from scipy import sparse
  from numpy.testing import assert_allclose, assert_equal
  from scipy.optimize import approx_fprime
label_desc: Use image node_id 1 for calling a global function with example usage: gen_simple_logit(nc, cs, s) and returns: y,  exog_fe,  exog_vc,  ident