code: def test_fit_joblib():
      # tests that the results of all the intermediate steps
      # remains correct for joblib fit, does this for OLS and GLM
      # and a variety of model sizes
      #
      # regression test
  
      np.random.seed(435265)
      X = np.random.normal(size=(50, 3))
      y = np.random.randint(0, 2, size=50)
  
      mod = DistributedModel(1, model_class=OLS)
      fit = mod.fit(
          _data_gen(y, X, 1),
          parallel_method="joblib",
          fit_kwds={"alpha": 0.5},
      )
      assert_allclose(
          fit.params,
          np.array([-0.191606, -0.012565, -0.351398]),
          atol=1e-6,
          rtol=0,
      )
      mod = DistributedModel(2, model_class=OLS)
      fit = mod.fit(
          _data_gen(y, X, 2),
          parallel_method="joblib",
          fit_kwds={"alpha": 0.5},
      )
      assert_allclose(
          fit.params,
          np.array([-0.157416, -0.029643, -0.471653]),
          atol=1e-6,
          rtol=0,
      )
      mod = DistributedModel(3, model_class=OLS)
      fit = mod.fit(
          _data_gen(y, X, 3),
          parallel_method="joblib",
          fit_kwds={"alpha": 0.5},
      )
      assert_allclose(
          fit.params,
          np.array([-0.124891, -0.050934, -0.403354]),
          atol=1e-6,
          rtol=0,
      )
  
      mod = DistributedModel(
          1, model_class=GLM, init_kwds={"family": Binomial()}
      )
      fit = mod.fit(
          _data_gen(y, X, 1),
          parallel_method="joblib",
          fit_kwds={"alpha": 0.5},
      )
      assert_allclose(
          fit.params,
          np.array([-0.164515, -0.412854, -0.223955]),
          atol=1e-6,
          rtol=0,
      )
      mod = DistributedModel(
          2, model_class=GLM, init_kwds={"family": Binomial()}
      )
      fit = mod.fit(
          _data_gen(y, X, 2),
          parallel_method="joblib",
          fit_kwds={"alpha": 0.5},
      )
      assert_allclose(
          fit.params,
          np.array([-0.142513, -0.360324, -0.295485]),
          atol=1e-6,
          rtol=0,
      )
      mod = DistributedModel(
          3, model_class=GLM, init_kwds={"family": Binomial()}
      )
      fit = mod.fit(
          _data_gen(y, X, 3),
          parallel_method="joblib",
          fit_kwds={"alpha": 0.5},
      )
      assert_allclose(
          fit.params,
          np.array([-0.110487, -0.306431, -0.243921]),
          atol=1e-6,
          rtol=0,
      )
  
imports: import numpy
  from numpy.testing import assert_equal, assert_, assert_allclose
  from statsmodels.regression.linear_model import OLS
  from statsmodels.genmod.generalized_linear_model import GLM
  from statsmodels.genmod.families import Binomial
  from statsmodels.base.distributed_estimation import _calc_grad, _calc_wdesign_mat, _est_regularized_debiased, _join_debiased, _est_regularized_naive, _est_unregularized_naive, _join_naive, DistributedModel
label_desc: Use image node_id 10 for calling a global function with example usage: test_fit_joblib() without return types