code: def test_2factor():
      """
      # R code:
      r = 0.4
      p = 6
      ii = seq(0, p-1)
      ii = outer(ii, ii, "-")
      ii = abs(ii)
      cm = r^ii
      factanal(covmat=cm, factors=2)
      """
  
      r = 0.4
      p = 6
      ii = np.arange(p)
      cm = r ** np.abs(np.subtract.outer(ii, ii))
  
      fa = Factor(corr=cm, n_factor=2, nobs=100, method="ml")
      rslt = fa.fit()
  
      for j in 0, 1:
          if rslt.loadings[0, j] < 0:
              rslt.loadings[:, j] *= -1
  
      uniq = np.r_[0.782, 0.367, 0.696, 0.696, 0.367, 0.782]
      assert_allclose(uniq, rslt.uniqueness, rtol=1e-3, atol=1e-3)
  
      loads = [
          np.r_[0.323, 0.586, 0.519, 0.519, 0.586, 0.323],
          np.r_[0.337, 0.538, 0.187, -0.187, -0.538, -0.337],
      ]
      for k in 0, 1:
          if np.dot(loads[k], rslt.loadings[:, k]) < 0:
              loads[k] *= -1
          assert_allclose(
              loads[k], rslt.loadings[:, k], rtol=1e-3, atol=1e-3
          )
  
      assert_equal(rslt.df, 4)
  
      # Smoke test for standard errors
      e = np.asarray(
          [
              0.11056836,
              0.05191071,
              0.09836349,
              0.09836349,
              0.05191071,
              0.11056836,
          ]
      )
      assert_allclose(rslt.uniq_stderr, e, atol=1e-4)
      e = np.asarray(
          [
              [0.08842151, 0.08842151],
              [0.06058582, 0.06058582],
              [0.08339874, 0.08339874],
              [0.08339874, 0.08339874],
              [0.06058582, 0.06058582],
              [0.08842151, 0.08842151],
          ]
      )
      assert_allclose(rslt.load_stderr, e, atol=1e-4)
  
file_path: statsmodels/statsmodels/multivariate/tests/test_ml_factor.py
imports: import numpy
  from statsmodels.multivariate.factor import Factor
  from numpy.testing import assert_allclose, assert_equal
  from scipy.optimize import approx_fprime
  import warnings
label_desc: Use image node_id 9 for calling a global function with example usage: test_2factor() without return types