Question

我正在进行主成分分析，并且我被告知缩放1的向量应该是长度为1.这里它们比1大得多。在缩放2中，它假设小于1。

我做错了吗？

另外，如果数据被标准化以在比例2中绘制描述符的平衡圆，是否有可能？

数据是对不同种类鸟类的喙测量。

数据集看起来像这样（名为pca.bird.clean）：

                 MBL             MBW             MBD
1               9.13            7.21            7.55
2              13.97           12.73           14.33
3               8.15            6.43            7.01
4              10.80            9.35           10.02
5                ...             ...             ...

PCA：

pca.all.sp=vegan::rda(pca.bird.clean[,c("MBL","MBW", "MBD")], scale=FALSE)

这是生成图像的代码（see here）

cleanplot.pca(pca.all.sp)

这是一个完全可重复的例子：

library(vegan)
nb.ind.per.sp = 100
nb.sp = rep(nb.ind.per.sp,4)
nind = sum(nb.sp)
sp.id = rep(c(1,2,3,4),each=nb.ind.per.sp)
nsp=4
nb.trait = 3 
mu.trait  =  structure(list(bird1 = c(9.83, 11.64, 11.09),
                            bird2 = c(6.84, 8.51, 7.09),
                            bird3 = c(13.17, 14.48, 15.27),
                            bird4 = c(8.26, 14.21, 8.59)),
                       .Names = c("bird1", "bird2", "bird3", "bird4"),
                       row.names = c("MBW_mean", "MBL_mean", "MBD_mean"), class = "data.frame")
sigma.trait= structure(list(bird1 = c(0.99, 0.94, 1.75),
                            bird2 = c(0.10, 0.22, 0.16), #c(0.10, 0.22, 0.16)
                            bird3 = c(0.98, 0.76, 1.99),
                            bird4 = c(0.19, 0.89, 0.29)), # c(0.19, 0.89, 0.29)
                       .Names = c("bird1", "bird2", "bird3", "bird4"),
                       row.names = c("MBW_var", "MBL_var", "MBD_var"), class = "data.frame")

ind.trait <- matrix(0, nrow=nind, ncol=dim(mu.trait)[1])
nb.id.sp.last <- 1 
for(nb.id.sp in 1:nsp) { 
  nb.id.sp.seq <- as.numeric(summary(as.factor(sp.id))[nb.id.sp]) 
  for(nbtraits in 1:(dim(mu.trait)[1])) {
    traits <- rnorm(n=nb.id.sp.seq,
                    mean = mu.trait[nbtraits,nb.id.sp], 
                    sd = sigma.trait[nbtraits,nb.id.sp])
    ind.trait[nb.id.sp.last:(nb.id.sp.last+nb.id.sp.seq-1),nbtraits] = traits 
  }
  nb.id.sp.last <- nb.id.sp.last + nb.id.sp.seq 
}
colnames(ind.trait) = c("MBW","MBL","MBD")
pca.all.sp=vegan::rda(ind.trait[,], scale=FALSE)

"cleanplot.pca" <- function(res.pca, ax1=1, ax2=2, point=FALSE, 
                            ahead=0.07, cex=0.7) 
{
  # A function to draw two biplots (scaling 1 and scaling 2) from an object 
  # of class "rda" (PCA or RDA result from vegan's rda() function)
  #
  # License: GPL-2 
  # Authors: Francois Gillet & Daniel Borcard, 24 August 2012

  require("vegan")

  par(mfrow=c(1,2))
  p <- length(res.pca$CA$eig)

  # Scaling 1: "species" scores scaled to relative eigenvalues
  sit.sc1 <- scores(res.pca, display="wa", scaling=1, choices=c(1:p))
  spe.sc1 <- scores(res.pca, display="sp", scaling=1, choices=c(1:p))
  plot(res.pca, choices=c(ax1, ax2), display=c("wa", "sp"), type="n", 
       main="PCA - scaling 1", scaling=1)
  if (point)
  {
    points(sit.sc1[,ax1], sit.sc1[,ax2], pch=20)
    text(res.pca, display="wa", choices=c(ax1, ax2), cex=cex, pos=3, scaling=1)
  }
  else
  {
    text(res.pca, display="wa", choices=c(ax1, ax2), cex=cex, scaling=1)
  }
  text(res.pca, display="sp", choices=c(ax1, ax2), cex=cex, pos=4, 
       col="red", scaling=1)
  arrows(0, 0, spe.sc1[,ax1], spe.sc1[,ax2], length=ahead, angle=20, col="red")
  pcacircle(res.pca)

  # Scaling 2: site scores scaled to relative eigenvalues
  sit.sc2 <- scores(res.pca, display="wa", choices=c(1:p))
  spe.sc2 <- scores(res.pca, display="sp", choices=c(1:p))
  plot(res.pca, choices=c(ax1,ax2), display=c("wa","sp"), type="n", 
       main="PCA - scaling 2")
  if (point) {
    points(sit.sc2[,ax1], sit.sc2[,ax2], pch=20)
    text(res.pca, display="wa", choices=c(ax1 ,ax2), cex=cex, pos=3)
  }
  else
  {
    text(res.pca, display="wa", choices=c(ax1, ax2), cex=cex)
  }
  text(res.pca, display="sp", choices=c(ax1, ax2), cex=cex, pos=4, col="red")
  arrows(0, 0, spe.sc2[,ax1], spe.sc2[,ax2], length=ahead, angle=20, col="red")
}



"pcacircle" <- function (pca) 
{
  # Draws a circle of equilibrium contribution on a PCA plot 
  # generated from a vegan analysis.
  # vegan uses special constants for its outputs, hence 
  # the 'const' value below.

  eigenv <- pca$CA$eig
  p <- length(eigenv)
  n <- nrow(pca$CA$u)
  tot <- sum(eigenv)
  const <- ((n - 1) * tot)^0.25
  radius <- (2/p)^0.5
  radius <- radius * const
  symbols(0, 0, circles=radius, inches=FALSE, add=TRUE, fg=2)
}

cleanplot.pca(pca.all.sp)

相关双标图（比例2）和距离双标图（比例1）PCA在R中的长度不正确

0 个答案: