code: def test_compare_numdiff(self, use_sqrt, reml, profile_fe):
      n_grp = 200
      grpsize = 5
      k_fe = 3
      k_re = 2
  
      np.random.seed(3558)
      exog_fe = np.random.normal(size=(n_grp * grpsize, k_fe))
      exog_re = np.random.normal(size=(n_grp * grpsize, k_re))
      exog_re[:, 0] = 1
      exog_vc = np.random.normal(size=(n_grp * grpsize, 3))
      slopes = np.random.normal(size=(n_grp, k_re))
      slopes[:, -1] *= 2
      slopes = np.kron(slopes, np.ones((grpsize, 1)))
      slopes_vc = np.random.normal(size=(n_grp, 3))
      slopes_vc = np.kron(slopes_vc, np.ones((grpsize, 1)))
      slopes_vc[:, -1] *= 2
      re_values = (slopes * exog_re).sum(1)
      vc_values = (slopes_vc * exog_vc).sum(1)
      err = np.random.normal(size=n_grp * grpsize)
      endog = exog_fe.sum(1) + re_values + vc_values + err
      groups = np.kron(range(n_grp), np.ones(grpsize))
  
      vc = {"a": {}, "b": {}}
      for i in range(n_grp):
          ix = np.flatnonzero(groups == i)
          vc["a"][i] = exog_vc[ix, 0:2]
          vc["b"][i] = exog_vc[ix, 2:3]
  
      with pytest.warns(UserWarning, match="Using deprecated variance"):
          model = MixedLM(
              endog,
              exog_fe,
              groups,
              exog_re,
              exog_vc=vc,
              use_sqrt=use_sqrt,
          )
      rslt = model.fit(reml=reml)
  
      loglike = loglike_function(
          model, profile_fe=profile_fe, has_fe=not profile_fe
      )
  
      try:
          # Test the score at several points.
          for kr in range(5):
              fe_params = np.random.normal(size=k_fe)
              cov_re = np.random.normal(size=(k_re, k_re))
              cov_re = np.dot(cov_re.T, cov_re)
              vcomp = np.random.normal(size=2) ** 2
              params = MixedLMParams.from_components(
                  fe_params, cov_re=cov_re, vcomp=vcomp
              )
              params_vec = params.get_packed(
                  has_fe=not profile_fe, use_sqrt=use_sqrt
              )
  
              # Check scores
              gr = -model.score(params, profile_fe=profile_fe)
              ngr = nd.approx_fprime(params_vec, loglike)
              assert_allclose(gr, ngr, rtol=1e-3)
  
          # Check Hessian matrices at the MLE (we do not have
          # the profile Hessian matrix and we do not care
          # about the Hessian for the square root
          # transformed parameter).
          if (profile_fe is False) and (use_sqrt is False):
              hess, sing = model.hessian(rslt.params_object)
              if sing:
                  pytest.fail("hessian should not be singular")
              hess *= -1
              params_vec = rslt.params_object.get_packed(
                  use_sqrt=False, has_fe=True
              )
              loglike_h = loglike_function(
                  model, profile_fe=False, has_fe=True
              )
              nhess = nd.approx_hess(params_vec, loglike_h)
              assert_allclose(hess, nhess, rtol=1e-3)
      except AssertionError:
          # See GH#5628; because this test fails unpredictably but only on
          #  OSX, we only xfail it there.
          if PLATFORM_OSX:
              pytest.xfail(
                  "fails on OSX due to unresolved "
                  "numerical differences"
              )
          else:
              raise
  
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 1 for calling the TestMixedLM obj's underlying member method code with example usage: obj.test_compare_numdiff(use_sqrt, reml, profile_fe) without return types