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  • $\begingroup$ I initially tried using a GLM with a Gamma log link to model non-linearity between the predictors and the outcome. After double-checking the model with posterior predictive checks, I concluded that the GLM was valid. However, I suspect that the predictors themselves are also non-linearly related to the outcome, which is why simply using a GLM with a log link function may not capture the complexity of the data. $\endgroup$ Commented Mar 25, 2025 at 22:30
  • $\begingroup$ To address this, I attempted to implement splines to model the non-linear relationships, but the results were inconsistent. Every time I broke the model into smaller pieces using splines, I obtained very different results, suggesting instability in the model. This indicates that the model may be overfitting or that the spline's flexibility is too high for the data, leading to instability. Thus, I need to further explore how to stabilize the model, possibly by using regularization or adjusting the number of knots in the splines. $\endgroup$ Commented Mar 25, 2025 at 22:31
  • $\begingroup$ Do you have any suggestions for a functional form that could better capture the non-linearity in the data, or how I could proceed next to stabilize the model? I really appreciate your time and input:) $\endgroup$ Commented Mar 25, 2025 at 22:33
  • $\begingroup$ @Nikimiskata there are many types of splines. See this page for explanations and links. I suggest natural cubic regression splines, for which you predetermine the complexity of the fit via the number of knots. Section 2.4.5 of Frank Harrell's Regression Modeling Strategies explains them. For your data, 5 to 7 knots placed at appropriate quantiles of each predictor could be good choices. The rest of the book has a lot of useful information on regression modeling, summarized in Chapter 4. $\endgroup$ Commented Mar 26, 2025 at 19:29