code: def test_qif_fit(fam, cov_struct):
      np.random.seed(234234)
  
      n = 1000
      q = 4
      params = np.r_[1, -0.5, 0.2]
      x = np.random.normal(size=(n, len(params)))
      if isinstance(fam, families.Gaussian):
          e = np.kron(np.random.normal(size=n // q), np.ones(q))
          e = np.sqrt(0.5) * e + np.sqrt(
              1 - 0.5**2
          ) * np.random.normal(size=n)
          y = np.dot(x, params) + e
      elif isinstance(fam, families.Poisson):
          lpr = np.dot(x, params)
          mean = np.exp(lpr)
          y = np.random.poisson(mean)
      elif isinstance(fam, families.Binomial):
          lpr = np.dot(x, params)
          mean = 1 / (1 + np.exp(-lpr))
          y = (np.random.uniform(0, 1, size=n) < mean).astype(int)
      g = np.kron(np.arange(n // q), np.ones(q)).astype(int)
  
      model = QIF(y, x, groups=g, family=fam, cov_struct=cov_struct)
      rslt = model.fit()
  
      # Slack comparison to population values
      assert_allclose(rslt.params, params, atol=0.05, rtol=0.05)
  
      # Smoke test
      _ = rslt.summary()
  
file_path: statsmodels/statsmodels/genmod/tests/test_qif.py
imports: import numpy
  from numpy.testing import assert_allclose
  import pandas
  import pytest
  from statsmodels.genmod.qif import QIF, QIFIndependence, QIFExchangeable, QIFAutoregressive
  from statsmodels.tools.numdiff import approx_fprime
  from statsmodels.genmod import families
label_desc: Use image node_id 2 for calling a global function with example usage: test_qif_fit(fam, cov_struct) without return types