r 中非线性 PCA 的引导特征值

Question

我是运行 r 中的非线性 PCA，使用 homals 包。这是我用作示例的代码块：

res1 <- homals(data = mydata, rank = 1, ndim = 9, level = "nominal")
res1 <- rescale(res1)

我想在此分析中生成 1000 bootstrap 个特征值估计值（替换），但我无法弄清楚代码。有人有什么建议吗？

示例数据：

dput(head(mydata, 30))

structure(list(`W age` = c(45L, 43L, 42L, 36L, 19L, 38L, 21L, 
27L, 45L, 38L, 42L, 44L, 42L, 38L, 26L, 48L, 39L, 37L, 39L, 26L, 
24L, 46L, 39L, 48L, 40L, 38L, 29L, 24L, 43L, 31L), `W education` = c(1L, 
2L, 3L, 3L, 4L, 2L, 3L, 2L, 1L, 1L, 1L, 4L, 2L, 3L, 2L, 1L, 2L, 
2L, 2L, 3L, 3L, 4L, 4L, 4L, 2L, 4L, 4L, 4L, 1L, 3L), `H education` = c(3L, 
3L, 2L, 3L, 4L, 3L, 3L, 3L, 1L, 3L, 4L, 4L, 4L, 4L, 4L, 1L, 2L, 
2L, 1L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 2L, 4L), `N children` = c(10L, 
7L, 9L, 8L, 0L, 6L, 1L, 3L, 8L, 2L, 4L, 1L, 1L, 2L, 0L, 7L, 6L, 
8L, 5L, 1L, 0L, 1L, 1L, 5L, 8L, 1L, 0L, 0L, 8L, 2L), `W religion` = c(1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), `W employment` = c(1L, 
1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 
1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 1L), `H occupation` = c(3L, 
3L, 3L, 3L, 3L, 3L, 3L, 3L, 2L, 3L, 1L, 1L, 3L, 2L, 4L, 2L, 2L, 
2L, 2L, 4L, 3L, 1L, 1L, 1L, 3L, 1L, 1L, 2L, 2L, 1L), `Standard of living` = 
c(4L, 
4L, 3L, 2L, 3L, 2L, 2L, 4L, 2L, 3L, 3L, 4L, 3L, 3L, 1L, 4L, 4L, 
3L, 1L, 1L, 1L, 4L, 4L, 4L, 3L, 4L, 4L, 2L, 4L, 4L), Media = c(0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L), Contraceptive = c(1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L)), .Names = c("W age", 
"W education", "H education", "N children", "W religion", "W employment", 
"H occupation", "Standard of living", "Media", "Contraceptive"
), row.names = c(NA, 30L), class = "data.frame")
>

我获得了与 homals 包一起使用的重新缩放功能，以进行最佳缩放。这是函数：

rescale <- function(res) {
    # Rescale homals results to proper scaling
    n <- nrow(res$objscores)
    m <- length(res$catscores)
    res$objscores <- (n * m)^0.5 * res$objscores
    res$scoremat <- (n * m)^0.5 * res$scoremat
    res$catscores <- lapply(res$catscores, FUN = function(x) (n * m)^0.5 * x)
    res$cat.centroids <- lapply(res$cat.centroids, FUN = function(x) (n * m)^0.5 * x)
    res$low.rank <- lapply(res$low.rank, FUN = function(x) n^0.5 * x)
    res$loadings <- lapply(res$loadings, FUN = function(x) m^0.5 * x)
    res$discrim <- lapply(res$discrim, FUN = function(x) (n * m)^0.5 * x)
    res$eigenvalues <- n * res$eigenvalues
    return(res)
}

Answer 1

在 R 中 bootstrap 的标准方法是使用基础包 boot。
我对后面的代码不是很满意，因为它抛出了很多警告。但这可能是由于我测试过的数据集所致。我在 help("homals") 中使用了数据集和第三个示例。

我只有运行 10 bootstrap 个重复。

library(homals)
library(boot)

boot_eigen <- function(data, indices){
    d <- data[indices, ]
    res <- homals(d, active = c(rep(TRUE, 4), FALSE), sets = list(c(1,3,4),2,5))
    res$eigenvalues
}

data(galo)

set.seed(7578)    # Make the results reproducible
eig <- boot(galo, boot_eigen, R = 10)

eig
#
#ORDINARY NONPARAMETRIC BOOTSTRAP
#
#
#Call:
#boot(data = galo, statistic = boot_eigen, R = 10)
#
#
#Bootstrap Statistics :
#     original      bias    std. error
#t1* 0.1874958  0.03547116 0.005511776
#t2* 0.2210821 -0.02478596 0.005741331

colMeans(eig$t)
#[1] 0.2229669 0.1962961

如果这也不适用于您的情况运行，请说出来，我会删除答案。

编辑。

为了回答评论中的讨论，我更改了函数boot_eigen，对homals的调用现在跟在问题代码之后，在返回之前调用rescale .

boot_eigen <- function(data, indices){
    d <- data[indices, ]
    res <- homals(data = d, rank = 1, ndim = 9, level = "nominal")
    res <- rescale(res)
    res$eigenvalues
}

set.seed(7578)    # Make the results reproducible
eig <- boot(mydata, boot_eigen, R = 10)

r 中非线性 PCA 的引导特征值

Bootstrapping eigenvalues for nonlinear PCA in r

r

eigenvalue

pca

statistics-bootstrap