How to correct conditional Poisson standard errors for over-dispersion

Question

I want to estimate a conditional negative binomial model, which an economist might call a negative binomial model with individual fixed effects. I use Python and statsmodels, which has a conditional Poisson model but not a conditional negative binomial model, as far as I know. I want to follow Allison and Waterman to estimate a conditional Poisson model and correct standard errors for over-dispersion as follows:

A relatively simple approach is to estimate the β coefficients under the fixed-effects Poisson model, but adjust the standard errors upward for overdispersion. A commonly-used adjustment is to multiply the standard errors by the square root of the ratio of the goodness-of-fit chi-square to the degrees of freedom. (Either Pearson’s chi-square or the deviance could be used. )

However, I can't find Pearson's $\chi^2$ in the output of statsmodels' ConditionalPoisson fit summary. A comment on a recent question suggests that I should separately estimate $\chi^2$. However, I don't see a fit method to estimate $\chi^2$, and the fit predict method (to manually calculate $\chi^2$) returns NotImplementedError.

How do I correct conditional Poisson standard errors in statsmodels for overdispersion?

Here's starter code:

import numpy as np
import pandas as pd
import statsmodels.discrete.conditional_models as cm

df = pd.DataFrame(
    {
        'i': (np.arange(10000) // 200) + 1,
        't': (np.arange(10000) % 200) + 1
    }
)

np.random.seed(2001)
df['x'] = np.random.normal(loc=df['i'])
df['y'] = np.random.negative_binomial(np.exp((df['i'] + df['x'])/10), 0.1)

df1 = df.groupby('i').filter(lambda x: x['y'].var() > 0)

m1 = cm.ConditionalPoisson(
    endog=df1['y'],
    exog=df1['x'],
    groups=df1['i']
)

f1 = m1.fit(method='newton', cov_type='cluster')

print(f1.summary())


                 Conditional Logit Model Regression Results                  
==============================================================================
Dep. Variable:                      y   No. Observations:                10000
Model:             ConditionalPoisson   No. groups:                         50
Log-Likelihood:           -1.1662e+09   Min group size:                    200
Method:                        newton   Max group size:                    200
Date:                Sat, 29 May 2021   Mean group size:                 200.0
Time:                        10:06:49                                         
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
x              0.1003   6.95e-05   1443.904      0.000       0.100       0.100
==============================================================================