Statsmodels中Poisson模型与泊松族GLM的差异及拟合问题咨询

Let’s break down the key distinctions between these two approaches, plus clear up that confusing behavior you noticed with regularization and model summaries.

Core Class & Design Differences #

• sm.Poisson: This is a specialized class built exclusively for Poisson regression. It inherits from Statsmodels' GenericLikelihoodModel, so it’s optimized specifically for maximum likelihood estimation (MLE) of Poisson models. It comes with small, Poisson-specific helper methods and attributes that aren’t available in the more general GLM class.
• sm.GLM: The Generalized Linear Model class is a flexible workhorse that supports all exponential family distributions (Poisson, Gaussian, Binomial, etc.) via the family parameter. Its default estimation method is iteratively reweighted least squares (IRLS), which works consistently across all supported families.

Estimation & Regularization Behavior #

Here’s where the quirk you observed comes into play:

• For sm.Poisson: The standard fit() method only runs vanilla MLE with no built-in regularization support. If you need L1/L2 regularization, you must use fit_regularize()—this method is purpose-built to add regularization to Poisson MLE, and it populates all the necessary attributes so summary() works as expected.
• For sm.GLM: The default fit() uses IRLS and generates a full summary with standard errors, p-values, and diagnostic stats. However, when you use fit_regularize(), the resulting model object skips computing most of the statistics that summary() relies on. This is a current limitation in Statsmodels—regularized GLM fits prioritize efficient coefficient estimation over generating a complete statistical summary, hence why summary() returns None.

When to Choose Which? #

• Go with sm.Poisson if you’re only working with Poisson regression and want a model tailored to that use case. Just remember to reach for fit_regularize() when you need regularization.
• Choose sm.GLM with family=sm.families.Poisson() if you want the flexibility to switch between different exponential family models later, or if you prefer the IRLS approach. If you use regularization here, be prepared to work with just the coefficients (since the summary won’t be available) and handle inference manually if needed.

Quick Recap of the "Odd" Behavior #

To wrap up that confusing quirk:

sm.Poisson requires fit_regularize() for regularization because its default fit() doesn’t support it, and this method is designed to maintain compatibility with summary().
sm.GLM’s fit_regularize() skips computing summary stats to optimize for regularization speed and efficiency, which is why calling summary() returns None.

内容的提问来源于stack exchange，提问作者ilikecats