code: def gbic(results, gbicp=False):
      """generalized BIC for misspecified models
  
      References
      ----------
      Lv, Jinchi, and Jun S. Liu. 2014. "Model Selection Principles in
      Misspecified Models." Journal of the Royal Statistical Society.
      Series B (Statistical Methodology) 76 (1): 141–67.
  
      """
      self = getattr(results, "_results", results)
      k_params = self.df_model + 1
      nobs = k_params + self.df_resid
      imr = getattr(results, "im_ratio", im_ratio(results))
      imr_logdet = np.linalg.slogdet(imr)[1]
      gbic = (
          -2 * self.llf + k_params * np.log(nobs) - imr_logdet
      )  # LL equ. (20)
      gbicp = gbic + np.trace(imr)  # LL equ. (23)
      return gbic, gbicp
  
file_path: statsmodels/statsmodels/base/_parameter_inference.py
imports: import numpy
  from scipy import stats
label_desc: Use image node_id 6 for calling a global function with example usage: gbic(results, gbicp) and returns: gbic,  gbicp