Generalized Linear Models › Model Diagnostics

Generalized Linear Models (GLMs) are highly flexible and powerful tools, but their effectiveness depends on how well they fit the data and whether their underlying assumptions hold. Thorough model diagnostics help evaluate the adequacy of a GLM, uncover potential issues, and guide improvements.

In traditional statistical modeling, diagnostics such as AIC/BIC, deviance residuals, and goodness-of-fit tests are used to assess model fit and to better understand the data-generating process. However, in many practical machine learning applications, our primary concern is predictive performance rather than detailed statistical inference. As a result, we often focus on how well the model generalizes to new, unseen data.

Note: This section provides only a high-level overview and does not cover the statistical inference aspects of GLMs, such as constructing confidence intervals or hypothesis testing, in detail. The focus is on practical model evaluation rather than formal statistical inference.

To evaluate predictive performance, we rely on common machine learning metrics such as F1 score, ROC AUC, log-loss, and calibration curves. These metrics help answer the most important question in applied settings: does the model make accurate and reliable predictions on data it hasn't seen before?

If your goal is to gain deeper insights into the data or understand the mechanisms behind the predictions, more advanced statistical diagnostics are valuable. This can include examining residuals, checking for outliers or influential points, and assessing the distribution of errors and standard errors of the estimates. These techniques can reveal model misspecification, violations of assumptions, or areas where the model could be improved.

The choice of diagnostics should be guided by your modeling goals: prioritize predictive metrics for practical applications, and use statistical diagnostics when interpretability and understanding of the data-generating process are important.