R-style formulas when implementing a power (i.e. square) in a GLM misbehaves

Question

In the python code below, the glm model specification does not include the third power in the in model1 but it does in model2:

model1 = glm(formula="wage ~ workhours + workhours**3           + C(gender)", data=df, family=sm.families.Gaussian())
model2 = glm(formula="wage ~ workhours + np.power(workhours, 3) + C(gender)", data=df, family=sm.families.Gaussian())

Is this a bug? According to the documentation **x raises something to the power 3.

Answer 1

** in a formula is treated as a formula operator, not as regular exponentiation. (This is similar to how ^ works in an R formula.)

(a+b+c+d)**3 means that the model should include a, b, c, d, and all interactions between these variables up to 3rd order.

workhours**3 means that the model should include workhours and all interactions between... just workhours... up to 3rd order... but there are no such interaction terms, so it's equivalent to just workhours.

In contrast, np.power(workhours, 3) is treated as Python code, and computes the power you wanted.

statsmodels uses patsy for formula handling, so for full details on the formula language, you can check the patsy docs.