典型相关分析(Canonical Correlation analysis, CCA)是研究两组变量之间相关关系的一种统计方法。如果每组变量中只包含一个变量,相关关系可以用相关系数来度量。但是每组变量中变量个数大于1时,比如A组温度和湿度两个变量,B组树高胸径两个变量,度量这两组变量之间的相关关系,可以利用主成分的思想,把两组变量的相关关系分别转化成两个综合变量的最大可能的相关关系,就是典型相关分析(CCA)。——摘自《应用统计分析与R语言实战》
以上图片出自教程http://my.ilstu.edu/~wjschne/444/CanonicalCorrelation.html#(4)
健康儿童形态 | 肺通气功能 |
---|---|
身高 x1 (cm) | 肺活量 y1 (L) |
体重 x2 (kg) | 静息通气 y2 (L) |
胸围 x3 (cm) | 每分钟最大通气量 y3 (L) |
df<-read.table("clipboard",header=T)
df
ndat<-scale(df)
A<-ndat[,1:3]
B<-ndat[,4:6]
res.ca<-cancor(A,B,xcenter=FALSE,ycenter = FALSE)
res.ca
研究人员感兴趣的是(Researchers are intersted in)心理变量和学术变量还有性别之间的关系是怎样的?特别的(In particular)。研究人员感兴趣的是需要多少维度(how many dimensions (canonical variables))来理解两组变量之间的关系
install.packages("GGally")
install.packages("CCA")
library(ggplot2)
library(GGally)
library(CCA)
mm<-read.csv("https://stats.idre.ucla.edu/stat/data/mmreg.csv")
head(mm)
colnames(mm)<-c("Control","Concept","Motivation","Read","Write","Math","Science","Gender")
summary(mm)
xtabs(~Gender,data=mm)
#输出结果
Gender
0 1
273 327
#
psych<-mm[,1:3]
acad<-mm[,4:8]
library(CCA)
matcor(psych,acad)
#输出结果
$Xcor
Control Concept Motivation
Control 1.0000000 0.1711878 0.2451323
Concept 0.1711878 1.0000000 0.2885707
Motivation 0.2451323 0.2885707 1.0000000
$Ycor
Read Write Math Science Gender
Read 1.00000000 0.6285909 0.6792757 0.6906929 -0.04174278
Write 0.62859089 1.0000000 0.6326664 0.5691498 0.24433183
Math 0.67927568 0.6326664 1.0000000 0.6495261 -0.04821830
Science 0.69069291 0.5691498 0.6495261 1.0000000 -0.13818587
Gender -0.04174278 0.2443318 -0.0482183 -0.1381859 1.00000000
$XYcor
Control Concept Motivation Read Write
Control 1.0000000 0.17118778 0.24513227 0.37356505 0.35887684
Concept 0.1711878 1.00000000 0.28857075 0.06065584 0.01944856
Motivation 0.2451323 0.28857075 1.00000000 0.21060992 0.25424818
Read 0.3735650 0.06065584 0.21060992 1.00000000 0.62859089
Write 0.3588768 0.01944856 0.25424818 0.62859089 1.00000000
Math 0.3372690 0.05359770 0.19501347 0.67927568 0.63266640
Science 0.3246269 0.06982633 0.11566948 0.69069291 0.56914983
Gender 0.1134108 -0.12595132 0.09810277 -0.04174278 0.24433183
Math Science Gender
Control 0.3372690 0.32462694 0.11341075
Concept 0.0535977 0.06982633 -0.12595132
Motivation 0.1950135 0.11566948 0.09810277
Read 0.6792757 0.69069291 -0.04174278
Write 0.6326664 0.56914983 0.24433183
Math 1.0000000 0.64952612 -0.04821830
Science 0.6495261 1.00000000 -0.13818587
Gender -0.0482183 -0.13818587 1.00000000
http://my.ilstu.edu/~wjschne/444/CanonicalCorrelation.html#(1)
http://ecology.msu.montana.edu/labdsv/R/labs/lab12/lab12.html#cats
http://www.sthda.com/english/articles/31-principal-component-methods-in-r-practical-guide/113-ca-correspondence-analysis-in-r-essentials/
http://userweb.eng.gla.ac.uk/umer.ijaz/bioinformatics/ecological.html 好长的R代码,必须要重复这篇
欢迎大家关注我的公众号
小明的数据分析笔记本