class_docstr: Class to contain results of fitting a linear mixed effects model.
  
  MixedLMResults inherits from statsmodels.LikelihoodModelResults
  
  Parameters
  ----------
  See statsmodels.LikelihoodModelResults
  
  Attributes
  ----------
  model : class instance
      Pointer to MixedLM model instance that called fit.
  normalized_cov_params : ndarray
      The sampling covariance matrix of the estimates
  params : ndarray
      A packed parameter vector for the profile parameterization.
      The first `k_fe` elements are the estimated fixed effects
      coefficients.  The remaining elements are the estimated
      variance parameters.  The variance parameters are all divided
      by `scale` and are not the variance parameters shown
      in the summary.
  fe_params : ndarray
      The fitted fixed-effects coefficients
  cov_re : ndarray
      The fitted random-effects covariance matrix
  bse_fe : ndarray
      The standard errors of the fitted fixed effects coefficients
  bse_re : ndarray
      The standard errors of the fitted random effects covariance
      matrix and variance components.  The first `k_re * (k_re + 1)`
      parameters are the standard errors for the lower triangle of
      `cov_re`, the remaining elements are the standard errors for
      the variance components.
  
  See Also
  --------
  statsmodels.LikelihoodModelResults
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docstr: Summarize the mixed model regression results.
  
  Parameters
  ----------
  yname : str, optional
      Default is `y`
  xname_fe : list[str], optional
      Fixed effects covariate names
  xname_re : list[str], optional
      Random effects covariate names
  title : str, optional
      Title for the top table. If not None, then this replaces
      the default title
  alpha : float
      significance level for the confidence intervals
  
  Returns
  -------
  smry : Summary instance
      this holds the summary tables and text, which can be
      printed or converted to various output formats.
  
  See Also
  --------
  statsmodels.iolib.summary2.Summary : class to hold summary results
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code: def summary(
      self,
      yname=None,
      xname_fe=None,
      xname_re=None,
      title=None,
      alpha=0.05,
  ):
      """
      Summarize the mixed model regression results.
  
      Parameters
      ----------
      yname : str, optional
          Default is `y`
      xname_fe : list[str], optional
          Fixed effects covariate names
      xname_re : list[str], optional
          Random effects covariate names
      title : str, optional
          Title for the top table. If not None, then this replaces
          the default title
      alpha : float
          significance level for the confidence intervals
  
      Returns
      -------
      smry : Summary instance
          this holds the summary tables and text, which can be
          printed or converted to various output formats.
  
      See Also
      --------
      statsmodels.iolib.summary2.Summary : class to hold summary results
      """
  
      from statsmodels.iolib import summary2
  
      smry = summary2.Summary()
  
      info = {}
      info["Model:"] = "MixedLM"
      if yname is None:
          yname = self.model.endog_names
  
      param_names = self.model.data.param_names[:]
      k_fe_params = len(self.fe_params)
      k_re_params = len(param_names) - len(self.fe_params)
  
      if xname_fe is not None:
          if len(xname_fe) != k_fe_params:
              msg = (
                  "xname_fe should be a list of length %d" % k_fe_params
              )
              raise ValueError(msg)
          param_names[:k_fe_params] = xname_fe
  
      if xname_re is not None:
          if len(xname_re) != k_re_params:
              msg = (
                  "xname_re should be a list of length %d" % k_re_params
              )
              raise ValueError(msg)
          param_names[k_fe_params:] = xname_re
  
      info["No. Observations:"] = str(self.model.n_totobs)
      info["No. Groups:"] = str(self.model.n_groups)
  
      gs = np.array([len(x) for x in self.model.endog_li])
      info["Min. group size:"] = "%.0f" % min(gs)
      info["Max. group size:"] = "%.0f" % max(gs)
      info["Mean group size:"] = "%.1f" % np.mean(gs)
  
      info["Dependent Variable:"] = yname
      info["Method:"] = self.method
      info["Scale:"] = self.scale
      info["Log-Likelihood:"] = self.llf
      info["Converged:"] = "Yes" if self.converged else "No"
      smry.add_dict(info)
      smry.add_title("Mixed Linear Model Regression Results")
  
      float_fmt = "%.3f"
  
      sdf = np.nan * np.ones((self.k_fe + self.k_re2 + self.k_vc, 6))
  
      # Coefficient estimates
      sdf[0 : self.k_fe, 0] = self.fe_params
  
      # Standard errors
      sdf[0 : self.k_fe, 1] = np.sqrt(
          np.diag(self.cov_params()[0 : self.k_fe])
      )
  
      # Z-scores
      sdf[0 : self.k_fe, 2] = (
          sdf[0 : self.k_fe, 0] / sdf[0 : self.k_fe, 1]
      )
  
      # p-values
      sdf[0 : self.k_fe, 3] = 2 * norm.cdf(
          -np.abs(sdf[0 : self.k_fe, 2])
      )
  
      # Confidence intervals
      qm = -norm.ppf(alpha / 2)
      sdf[0 : self.k_fe, 4] = (
          sdf[0 : self.k_fe, 0] - qm * sdf[0 : self.k_fe, 1]
      )
      sdf[0 : self.k_fe, 5] = (
          sdf[0 : self.k_fe, 0] + qm * sdf[0 : self.k_fe, 1]
      )
  
      # All random effects variances and covariances
      jj = self.k_fe
      for i in range(self.k_re):
          for j in range(i + 1):
              sdf[jj, 0] = self.cov_re[i, j]
              sdf[jj, 1] = np.sqrt(self.scale) * self.bse[jj]
              jj += 1
  
      # Variance components
      for i in range(self.k_vc):
          sdf[jj, 0] = self.vcomp[i]
          sdf[jj, 1] = np.sqrt(self.scale) * self.bse[jj]
          jj += 1
  
      sdf = pd.DataFrame(index=param_names, data=sdf)
      sdf.columns = [
          "Coef.",
          "Std.Err.",
          "z",
          "P>|z|",
          "[" + str(alpha / 2),
          str(1 - alpha / 2) + "]",
      ]
      for col in sdf.columns:
          sdf[col] = [
              float_fmt % x if np.isfinite(x) else "" for x in sdf[col]
          ]
  
      smry.add_df(sdf, align="r")
  
      return smry
  
imports: import warnings
  import numpy
  import pandas
  import patsy
  from scipy import sparse
  from scipy.stats.distributions import norm
  from statsmodels.base._penalties import Penalty
  import statsmodels.base.model
  from statsmodels.tools import data
  from statsmodels.tools.decorators import cache_readonly
  from statsmodels.tools.sm_exceptions import ConvergenceWarning
label_desc: Use image node_id 10 for calling the MixedLMResults obj's underlying member method code with example usage: obj.summary(yname, xname_fe, xname_re, title, alpha) and returns: smry