code: def test_vcomp_formula(self):
      np.random.seed(6241)
      n = 800
      exog = np.random.normal(size=(n, 2))
      exog[:, 0] = 1
      ex_vc = []
      groups = np.kron(np.arange(n / 4), np.ones(4))
      errors = 0
      exog_re = np.random.normal(size=(n, 2))
      slopes = np.random.normal(size=(n // 4, 2))
      slopes = np.kron(slopes, np.ones((4, 1))) * exog_re
      errors += slopes.sum(1)
      ex_vc = np.random.normal(size=(n, 4))
      slopes = np.random.normal(size=(n // 4, 4))
      slopes[:, 2:] *= 2
      slopes = np.kron(slopes, np.ones((4, 1))) * ex_vc
      errors += slopes.sum(1)
      errors += np.random.normal(size=n)
      endog = exog.sum(1) + errors
  
      exog_vc = {"a": {}, "b": {}}
      for k, group in enumerate(range(int(n / 4))):
          ix = np.flatnonzero(groups == group)
          exog_vc["a"][group] = ex_vc[ix, 0:2]
          exog_vc["b"][group] = ex_vc[ix, 2:]
      with pytest.warns(UserWarning, match="Using deprecated variance"):
          model1 = MixedLM(
              endog, exog, groups, exog_re=exog_re, exog_vc=exog_vc
          )
      result1 = model1.fit()
  
      df = pd.DataFrame(exog[:, 1:], columns=["x1"])
      df["y"] = endog
      df["re1"] = exog_re[:, 0]
      df["re2"] = exog_re[:, 1]
      df["vc1"] = ex_vc[:, 0]
      df["vc2"] = ex_vc[:, 1]
      df["vc3"] = ex_vc[:, 2]
      df["vc4"] = ex_vc[:, 3]
      vc_formula = {"a": "0 + vc1 + vc2", "b": "0 + vc3 + vc4"}
      model2 = MixedLM.from_formula(
          "y ~ x1",
          groups=groups,
          re_formula="0 + re1 + re2",
          vc_formula=vc_formula,
          data=df,
      )
      result2 = model2.fit()
  
      assert_allclose(result1.fe_params, result2.fe_params, rtol=1e-8)
      assert_allclose(result1.cov_re, result2.cov_re, rtol=1e-8)
      assert_allclose(result1.vcomp, result2.vcomp, rtol=1e-8)
      assert_allclose(result1.params, result2.params, rtol=1e-8)
      assert_allclose(result1.bse, result2.bse, rtol=1e-8)
  
imports: from statsmodels.compat.platform import PLATFORM_OSX
  import os
  import csv
  import warnings
  import numpy
  import pandas
  from scipy import sparse
  import pytest
  from statsmodels.regression.mixed_linear_model import MixedLM, MixedLMParams, _smw_solver, _smw_logdet
  from numpy.testing import assert_almost_equal, assert_equal, assert_allclose, assert_
  from statsmodels.base import _penalties
  import statsmodels.tools.numdiff
  from .results import lme_r_results
label_desc: Use image node_id 12 for calling the TestMixedLM obj's underlying member method code with example usage: obj.test_vcomp_formula() without return types