mgcv:如何返回估计的平滑参数? [英] mgcv: How to return estimated smoothing parameter?

问题描述

考虑简单的GAM拟合如下:

Consider the simple GAM fit as below:

library(mgcv)
my.gam <- gam(y~s(x), data=mydata)

1. 总有没有要返回估计的平滑参数(lambda)以便保存吗?我知道lambda在输出中以"GCV分数"给出，但是我需要一个特定的代码来返回它.
2. 如何将lambda设置为所需值?

推荐答案

summary()不返回平滑参数.您已将GCV得分与平滑参数混合在一起.如果您不了解这些概念，请咨询当地的统计学家，或者对交叉验证"提出疑问.我只会向您展示如何提取和设置平滑参数.

summary() does not return smoothing parameters. You have mixed up GCV score with smoothing parameter. Consult a local statistician if you don't understand those concepts, or raise a question on Cross Validated. I will only show you how to extract and set smoothing parameters.

考虑一个例子:

library(mgcv)
set.seed(2)
dat <- gamSim(1, n=400, dist="normal", scale=2)
b <- gam(y ~ s(x0) + s(x1) + s(x2) + s(x3), data=dat)

您可以从以下位置获取内部平滑参数:

You can get internal smoothing parameters from:

b$sp
#       s(x0)        s(x1)        s(x2)        s(x3) 
#3.648590e+00 3.850127e+00 1.252710e-02 4.986399e+10 

但是这些不是lambda.它们与lambda的区别在于某些正比例因子.使用sp平滑参数通常就足够了.如果要将其设置为固定值，请执行以下操作:

But these are not lambda. They differ from lambda by some positive scaling factors. It is usually sufficient to use sp for smoothing parameters. If you want to set it to a fixed value, do for example:

b1 <- gam(y ~ s(x0, sp = 0) + s(x1, sp = 0) + s(x2, sp = 0) + s(x3, sp = 0),
          data = dat)

这实际上禁用了所有平滑词的惩罚.请注意，将sp设置为负值意味着sp的自动选择.

This essentially disables penalization for all smooth terms. Note that setting sp to a negative value implies auto-selection of sp.

lambda和sp :

lambda and sp:

sapply(b$smooth, "[[", "S.scale") / b$sp
#       s(x0)        s(x1)        s(x2)        s(x3) 
#6.545005e+00 5.326938e+00 1.490702e+03 4.097379e-10 

有时需要获取lambda.当将平滑函数视为随机效果或随机字段时，有

Sometimes getting lambda is necessary. When considering smooth functions as random effects or random fields, there is

variance_parameter_of_random_effect = scale_parameter / lambda

在b$scale中可以找到scale参数(对于高斯模型，它也是b$sig2).查看相关问题:带有"gp"的GAM，更平滑:如何检索方差图参数?

where the scale parameter can be found in b$scale (for Gaussian model this is also b$sig2). See a related question: GAM with "gp" smoother: how to retrieve the variogram parameters?

跟进

是的，我需要lambda的确切值，因此感谢简洁的代码.但是我有兴趣进一步了解比例因子.除了包装手册外，我还能在哪里阅读更多有关它的信息?

Yes, I need the exact value of lambda, so thanks for the neat code. Yet I'm interested in knowing more about the scaling factor. Where can I read more about it in addition to the package manual?

请阅读?smoothCon:

smoothCon(object,data,knots=NULL,absorb.cons=FALSE,
          scale.penalty=TRUE,n=nrow(data),dataX=NULL,
          null.space.penalty=FALSE,sparse.cons=0,
          diagonal.penalty=FALSE,apply.by=TRUE,modCon=0)

scale.penalty: should the penalty coefficient matrix be scaled to have
          approximately the same 'size' as the inner product of the
          terms model matrix with itself? ...

在smoothCon的源代码中，有:

if (scale.penalty && length(sm$S) > 0 && is.null(sm$no.rescale)) {
    maXX <- norm(sm$X, type = "I")^2
    for (i in 1:length(sm$S)) {
        maS <- norm(sm$S[[i]])/maXX
        sm$S[[i]] <- sm$S[[i]]/maS
        sm$S.scale[i] <- maS
    }
}

简而言之，对于模型矩阵X和原始惩罚矩阵S，缩放因子maS为:

Briefly speaking, for a model matrix X and raw penalty matrix S, scaling factor maS is:

norm(S) / norm(X, type = "I")^2

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