GAM（廣義加法模型）是否存在共線性問題？

線性回歸方法存在共線性效應。例如，這個問題是關於 GLM 中的共線預測變量的。但是 GAM 是非線性的，在使用 GAM 之前我們是否需要檢查自變量的共線性？

GAM 模型可能會受到concurvity（GLM 共線性對 GAM 模型的擴展）的影響。

根據https://stat.ethz.ch/R-manual/R-devel/library/mgcv/html/concurvity.html：

"Concurvity occurs when some smooth term in a model could be approximated by     
one or more of the other smooth terms in the model. This is often the case     
when a smooth of space is included in a model, along with smooths of other      
covariates that also vary more or less smoothly in space. Similarly it tends   
to be an issue in models including a smooth of time, along with smooths of 
other time varying covariates.

Concurvity can be viewed as a generalization of co-linearity, and causes   
similar problems of interpretation. It can also make estimates somewhat 
unstable (so that they become sensitive to apparently innocuous modelling   
details, for example)."

上面的鏈接解釋瞭如何為裝有 R 中的 mgcv 包的 GAM 模型計算三種不同的曲率度量，所有這些都在 0 和 1 之間（0 表示沒有曲率）。

因此，您必須通過計算適當的彎曲度度量並確保它們不太高（即不太接近 1）來檢查 GAM 模型中潛在的彎曲度。另請參閱gam smoother 與參數項（曲率差異），https ://jroy042.github.io/nonlinear/week3.html和https://eric-pedersen.github.io/mgcv-esa-workshop/slides/02- model_checking.html#/。

引用自：https://stats.stackexchange.com/questions/400395