class_docstr: Results class for generalized additive models, GAM.
  
  This inherits from GLMResults.
  
  Warning: some inherited methods might not correctly take account of the
  penalization
  
  GLMGamResults inherits from GLMResults
  All methods related to the loglikelihood function return the penalized
  values.
  
  Attributes
  ----------
  
  edf
      list of effective degrees of freedom for each column of the design
      matrix.
  hat_matrix_diag
      diagonal of hat matrix
  gcv
      generalized cross-validation criterion computed as
      ``gcv = scale / (1. - hat_matrix_trace / self.nobs)**2``
  cv
      cross-validation criterion computed as
      ``cv = ((resid_pearson / (1 - hat_matrix_diag))**2).sum() / nobs``
  
  Notes
  -----
  status: experimental
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docstr: hypothesis test that a smooth component is zero.
  
  This calls `wald_test` to compute the hypothesis test, but uses
  effective degrees of freedom.
  
  Parameters
  ----------
  smooth_index : int
      index of the smooth term within list of smooth terms
  
  Returns
  -------
  wald_test : ContrastResults instance
      the results instance created by `wald_test`
docstr_tok: ["hypothesis","test","that","a","smooth","component","is","zero",".","This","calls","`","wald_test","`","to","compute","the","hypothesis","test",",","but","uses","effective","degrees","of","freedom",".","Parameters","--","--","--","--","--","smooth_index",":","int","index","of","the","smooth","term","within","list","of","smooth","terms","Returns","--","--","--","-","wald_test",":","ContrastResults","instance","the","results","instance","created","by","`","wald_test","`"]
code: def test_significance(self, smooth_index):
      """hypothesis test that a smooth component is zero.
  
      This calls `wald_test` to compute the hypothesis test, but uses
      effective degrees of freedom.
  
      Parameters
      ----------
      smooth_index : int
          index of the smooth term within list of smooth terms
  
      Returns
      -------
      wald_test : ContrastResults instance
          the results instance created by `wald_test`
      """
  
      variable = smooth_index
      smoother = self.model.smoother
      start_idx = self.model.k_exog_linear
  
      k_params = len(self.params)
      # a bit messy, we need first index plus length of smooth term
      mask = smoother.mask[variable]
      k_constraints = mask.sum()
      idx = start_idx + np.nonzero(mask)[0][0]
      constraints = np.eye(k_constraints, k_params, idx)
      df_constraints = self.edf[idx : idx + k_constraints].sum()
  
      return self.wald_test(constraints, df_constraints=df_constraints)
  
imports: from collections.abc import Iterable
  import copy
  import numpy
  from scipy import optimize
  import pandas
  import statsmodels.base.wrapper
  from statsmodels.discrete.discrete_model import Logit
  from statsmodels.genmod.generalized_linear_model import GLM, GLMResults, GLMResultsWrapper, _check_convergence
  import statsmodels.regression.linear_model
  from statsmodels.tools.sm_exceptions import PerfectSeparationError, ValueWarning
  from statsmodels.tools.decorators import cache_readonly
  from statsmodels.tools.data import _is_using_pandas
  from statsmodels.tools.linalg import matrix_sqrt
  from statsmodels.base._penalized import PenalizedMixin
  from statsmodels.gam.gam_penalties import MultivariateGamPenalty
  from statsmodels.gam.gam_cross_validation.gam_cross_validation import MultivariateGAMCVPath
  from statsmodels.gam.gam_cross_validation.cross_validators import KFold
label_desc: Use image node_id 7 for calling the GLMGamResults obj's underlying member method code with example usage: obj.test_significance(smooth_index) and returns: self