I am trying to build a GLM model (poisson family) using python statsmodels package on train data. The data I have contains categorical values as exogenous variables and numerical values for my target (endegenous variable). I did standardization for numeric values and one-hot-encoding on categorical values (drop the first level). When I fit the data into the model, I got the following exceptions :

ValueError: NaN, inf or invalid value detected in endog, 
estimation infeasible.  

The error comes when creating this model :

poisson_model = sm.GLM(endog=y_train, exog=X_train_std, 
   offset = np.log(X_train_std.EXPOSITION))

The problem comes from np.log(X_train_std.EXPOSITION) since I can not apply log function on zero values. But I don't know how to correct the error. I need to take into consideration the offset and when changing its link function to identy I get EXPOSITION in the GLM output.

Any help please ? How to deal with offset that takes 0 values with a log link function ?

  • $\begingroup$ What do you mean by "standardization" of the numeric value, subtracting the mean and then dividing by the standard deviation? $\endgroup$
    – Dave
    Feb 9, 2022 at 17:44
  • $\begingroup$ Yes, I meant that. $\endgroup$ Feb 9, 2022 at 17:46
  • $\begingroup$ Is the response y_train always zero in the cases where X_train_std.EXPOSITION is zero? $\endgroup$ Feb 9, 2022 at 20:25
  • 2
    $\begingroup$ X_train_std.EXPOSITION is like exposure in the Poisson model. With zero exposure, there should not be any counts. In that case, dropping those observations seems appropriate. $\endgroup$
    – Josef
    Feb 9, 2022 at 20:29

1 Answer 1


Standardization means that you subtract the mean $\bar y$ and then divide by the standard deviation $s_y$.

$$ z_i = \dfrac{y_i - \bar y}{s_y} $$

By doing this transformation (unless all $y_i$ are equal, which not an interesting scenario), you create $z_i$ values less than zero, which are out of bounds in Poisson regression. This is what the error message is telling you.

(You also create $z_i$ values that are not even integers! Again, such values are out of bounds in Poisson regression.)

  • $\begingroup$ Clear enough ! Thank you for the explanantion. In this case, can I ignore standardization since I have one only numeric variable which is my offset variable ? $\endgroup$ Feb 10, 2022 at 15:39
  • $\begingroup$ I do not follow what you mean by an offset variable. @KarimaTouati $\endgroup$
    – Dave
    Feb 10, 2022 at 15:42
  • $\begingroup$ I mean weight variable // exposure.. $\endgroup$ Feb 10, 2022 at 15:43
  • $\begingroup$ Non-integers can make sense for Poisson regression. Some implementations do accept them. $\endgroup$
    – Nick Cox
    Nov 13, 2023 at 16:30

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