r - 为什么从 glmnet 模型中获取回归系数的统计摘要信息是不可取的？

Question

我有一个二元结果的回归模型。我用 glmnet 拟合了模型并得到了选定的变量及其系数。

由于 glmnet 不计算变量的重要性，我想将确切的输出(选定的变量及其系数)提供给 glm 以获取信息(标准错误等)。

我搜索了 r 文档，看来我可以使用 glm 中的“方法”选项来指定用户定义的函数。
但是我没有这样做，有人可以帮助我吗？

Answer 1

"It is a very natural question to ask for standard errors of regression coefficients or other estimated quantities. In principle such standard errors can easily be calculated, e.g. using the bootstrap.

Still, this package deliberately does not provide them. The reason for this is that standard errors are not very meaningful for strongly biased estimates such as arise from penalized estimation methods. Penalized estimation is a procedure that reduces the variance of estimators by introducing substantial bias. The bias of each estimator is therefore a major component of its mean squared error, whereas its variance may contribute only a small part.

Unfortunately, in most applications of penalized regression it is impossible to obtain a sufficiently precise estimate of the bias. Any bootstrap-based calculations can only give an assessment of the variance of the estimates. Reliable estimates of the bias are only available if reliable unbiased estimates are available, which is typically not the case in situations in which penalized estimates are used.

Reporting a standard error of a penalized estimate therefore tells only part of the story. It can give a mistaken impression of great precision, completely ignoring the inaccuracy caused by the bias. It is certainly a mistake to make confidence statements that are only based on an assessment of the variance of the estimates, such as bootstrap-based confidence intervals do."

Jelle Goeman, Ph.D. Leiden University, Author of the Penalized package in R.