code: def test_profile_inference(self):
      np.random.seed(9814)
      k_fe = 2
      gsize = 3
      n_grp = 100
      exog = np.random.normal(size=(n_grp * gsize, k_fe))
      exog_re = np.ones((n_grp * gsize, 1))
      groups = np.kron(np.arange(n_grp), np.ones(gsize))
      vca = np.random.normal(size=n_grp * gsize)
      vcb = np.random.normal(size=n_grp * gsize)
      errors = 0
      g_errors = np.kron(np.random.normal(size=100), np.ones(gsize))
      errors += g_errors + exog_re[:, 0]
      rc = np.random.normal(size=n_grp)
      errors += np.kron(rc, np.ones(gsize)) * vca
      rc = np.random.normal(size=n_grp)
      errors += np.kron(rc, np.ones(gsize)) * vcb
      errors += np.random.normal(size=n_grp * gsize)
  
      endog = exog.sum(1) + errors
      vc = {"a": {}, "b": {}}
      for k in range(n_grp):
          ii = np.flatnonzero(groups == k)
          vc["a"][k] = vca[ii][:, None]
          vc["b"][k] = vcb[ii][:, None]
      with pytest.warns(UserWarning, match="Using deprecated variance"):
          rslt = MixedLM(
              endog, exog, groups=groups, exog_re=exog_re, exog_vc=vc
          ).fit()
      rslt.profile_re(
          0, vtype="re", dist_low=1, num_low=3, dist_high=1, num_high=3
      )
      rslt.profile_re(
          "b",
          vtype="vc",
          dist_low=0.5,
          num_low=3,
          dist_high=0.5,
          num_high=3,
      )
  
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 4 for calling the TestMixedLM obj's underlying member method code with example usage: obj.test_profile_inference() without return types