Error when performing autoregressive GEE in Python

Question

Although this question is a programming question and would, therefore, be more suitable for StackOverflow, I would like to address the question over here given that it is the result of a rather unknown method for non-statisticians, and I was hoping other people may have encountered the same issue.

I am testing the GEE with a small dataset in Python. When I use the independent or exchangeable covariance matrix, it works perfectly fine. However, when I attempt to use the autoregressive covariance matrix, I get a # ValueError: Not a bracketing interval. What may be the reason for that error?

The dataset consists of several different variables, but has only five samples. In the GEE, I use one group, and the time variable is the cumulative sum of dur_int_sec:

    eda_t_filt         SDNN  dur_int_sec
0    -0.181794   126.970082    65.691406 
1     0.130116   130.083402    98.619141
2    -0.106355   113.451393   129.865234
3     0.005535    90.197269   343.261719
4     0.013384   112.712131   241.161132

# The code
ar = sm.cov_struct.Autoregressive()
gee_by_task_ar = sm.GEE.from_formula("SDNN ~ eda_t_filt", \    
    groups=np.ones(5), data=by_task, time=np.cumsum(by_task.dur_int_sec), cov_struct=ar)
gee_by_task_ar_res = gee_by_task_ar.fit() # ValueError: Not a bracketing interval.

---

The complete error:

Traceback (most recent call last):
  File "<pyshell#50>", line 1, in <module>
    gee_by_task__ar_res = gee_by_task_ar.fit() # ValueError: Not a bracketing interval.
  File "D:\Python27\lib\site-packages\statsmodels\genmod\generalized_estimating_equations.py", line 1113, in fit
    self._update_assoc(mean_params)
  File "D:\Python27\lib\site-packages\statsmodels\genmod\generalized_estimating_equations.py", line 1261, in _update_assoc
    self.cov_struct.update(params)
  File "D:\Python27\lib\site-packages\statsmodels\genmod\cov_struct.py", line 768, in update
    self.dep_params = brent(fitfunc, brack=[b_lft, b_ctr, b_rgt])
  File "D:\Python27\lib\site-packages\scipy\optimize\optimize.py", line 2003, in brent
    res = _minimize_scalar_brent(func, brack, args, **options)
  File "D:\Python27\lib\site-packages\scipy\optimize\optimize.py", line 2035, in _minimize_scalar_brent
    brent.optimize()
  File "D:\Python27\lib\site-packages\scipy\optimize\optimize.py", line 1841, in optimize
    xa, xb, xc, fa, fb, fc, funcalls = self.get_bracket_info()
  File "D:\Python27\lib\site-packages\scipy\optimize\optimize.py", line 1829, in get_bracket_info
    raise ValueError("Not a bracketing interval.")
ValueError: Not a bracketing interval.

Answer 1

The variables in your model formula do not exist in the data you provided, so I'm not sure what you are trying to do here.

But in general, I have seen this AR covariance structure fail when the data are a poor fit to the AR model. The error message could be improved, but I suspect that is what is going on here.