code: def test_simple_logit_map():
      y, exog_fe, exog_vc, ident = gen_simple_logit(10, 10, 2)
      exog_vc = sparse.csr_matrix(exog_vc)
  
      glmm = BinomialBayesMixedGLM(
          y, exog_fe, exog_vc, ident, vcp_p=0.5
      )
      rslt = glmm.fit_map()
  
      assert_allclose(
          glmm.logposterior_grad(rslt.params),
          np.zeros_like(rslt.params),
          atol=1e-3,
      )
  
      # Test the predict method
      for linear in False, True:
          for exog in None, exog_fe:
              pr1 = rslt.predict(linear=linear, exog=exog)
              pr2 = glmm.predict(rslt.params, linear=linear, exog=exog)
              assert_allclose(pr1, pr2)
              if not linear:
                  assert_equal(pr1.min() >= 0, True)
                  assert_equal(pr1.max() <= 1, True)
  
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 6 for calling a global function with example usage: test_simple_logit_map() without return types