GAM(广义加法模型)是否存在共线性问题?

机器算法验证 广义线性模型 广义加法模型
2022-03-29 14:20:07

线性回归方法存在共线性效应。例如,这个问题是关于 GLM 中的共线预测变量的。但是 GAM 是非线性的,在使用 GAM 之前我们是否需要检查自变量的共线性?

1个回答

GAM 模型可能会受到concurvity(GLM 共线性对 GAM 模型的扩展)的影响。

根据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)."

上面的链接解释了如何为安装了 R 中的 mgcv 包的 GAM 模型计算三种不同的曲率度量,所有这些都在 0 和 1 之间(0 表示没有曲率)。

因此,您必须通过计算适当的弯曲度度量并确保它们不太高(即不太接近 1)来检查 GAM 模型中潜在的弯曲度。另请参阅gam smoother 与参数项(曲率差异)https ://jroy042.github.io/nonlinear/week3.html和https://eric-pedersen.github.io/mgcv-esa-workshop/slides/02- model_checking.html#/