code: def test_1factor():
      """
      # R code:
      r = 0.4
      p = 4
      ii = seq(0, p-1)
      ii = outer(ii, ii, "-")
      ii = abs(ii)
      cm = r^ii
      fa = factanal(covmat=cm, factors=1)
      print(fa, digits=10)
      """
  
      r = 0.4
      p = 4
      ii = np.arange(p)
      cm = r ** np.abs(np.subtract.outer(ii, ii))
  
      fa = Factor(corr=cm, n_factor=1, method="ml")
      rslt = fa.fit()
  
      if rslt.loadings[0, 0] < 0:
          rslt.loadings[:, 0] *= -1
  
      # R solution, but our likelihood is higher
      # uniq = np.r_[0.8392472054, 0.5820958187, 0.5820958187, 0.8392472054]
      # load = np.asarray([[0.4009399224, 0.6464550935, 0.6464550935,
      #                     0.4009399224]]).T
      # l1 = fa.loglike(fa._pack(load, uniq))
      # l2 = fa.loglike(fa._pack(rslt.loadings, rslt.uniqueness))
  
      # So use a smoke test
      uniq = np.r_[0.85290232, 0.60916033, 0.55382266, 0.82610666]
      load = np.asarray(
          [[0.38353316], [0.62517171], [0.66796508], [0.4170052]]
      )
  
      assert_allclose(load, rslt.loadings, rtol=1e-3, atol=1e-3)
      assert_allclose(uniq, rslt.uniqueness, rtol=1e-3, atol=1e-3)
  
      assert_equal(rslt.df, 2)
  
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 8 for calling a global function with example usage: test_1factor() without return types