【Mathematical Modeling】--Canonical Correlation Analysis

Canonical Correlation Analysis (Canonical Correlation Analysis) is a multivariate statistical method that studies the correlation between two groups of variables (each group of variables may have multiple indicators). It can reveal the inner connection between two sets of variables.

example:

 

Canonical correlation analysis definition:

Column title analysis:

Ideas:

Multivariate statistics: (this part is only for some understanding, the blogger is still involved in statistical probability, so he can only put some ppt)

1. introduction:
2. The basic idea of ​​canonical correlation analysis:

 

 

(The following two pictures conform to the ka square test of our high school mathematics.) When the calculation result <ka square, there is no correlation, otherwise there is a correlation.

 

Standardized related variables:

Typical load analysis:

Typical redundancy analysis:

                                                                        

Key steps in canonical correlation analysis:

 

             

Application of canonical correlation analysis in spss

(We usually use spss to help us calculate and count when solving problems)

step:

 

 

After spss is exported, if you want to write it in a paper, you need to modify some names:

Change the typical correlation to -> typical correlation coefficient, significance -> p value

Standardized canonical correlation coefficient -> linear combination corresponding to standardized canonical correlation variables

Let's talk about the initial TV score as an example using spss:

GET DATA

  /TYPE=XLSX

  /FILE='C:\Users\kay21\OneDrive\Documents\Canonical Correlation Analysis.xlsx'

  /SHEET=name 'Sheet1'

  /CELLRANGE=FULL

  /READNAMES=ON

  /DATATYPEMIN PERCENTAGE=95.0

  /HIDDEN IGNORE=YES.

EXECUTE.

DATASET NAME Dataset 1 WINDOW=FRONT.

STATS CANCORR SET1=led hed net   SET2=arti com man

/OPTIONS  COMPUTECVARS=NO

/PRINT PAIRWISECORR=NO LOADINGS=YES VARPROP=YES COEFFICIENTS=YES.

Canonical Correlations

Remark
Output created		19-JUL-2023 10:45:14
note
enter	active dataset	Dataset 1
	filter	<none> _
	Weights	<none> _
	split file	<none> _
grammar		BEGIN PROGRAM '#        '.
resource	handler time	00:00:00.02
	time consuming	00:00:00.05

[Dataset 1]

Typical Correlation Settings
	value
set1 variable	led hed net
Set 2 variables	art with man
centralized data set	none
Grading Grammar	none
Relevance for Scoring	3

canonical correlation coefficient
	Correlation	Eigenvalues	Wilk Statistics	F	Molecular degrees of freedom	denominator degrees of freedom	P value
1	.995	108.911	.000	141.580	9.000	58.560	.000
2	.953	9.854	.055	40.940	4.000	50.000	.000
3	.637	.684	.594	17.784	1.000	26.000	.000

H0 for Wilks test means that the correlation is zero in the current and subsequent rows

The linear combination corresponding to the standardized canonical correlation variables of set 1
variable	1	2	3
led	.149	-.786	-1.212
hed	.977	.383	-.160
net	-.052	-.312	1.467

Set 2 Linear combinations corresponding to standardized canonical correlated variables
variable	1	2	3
arti	.858	.911	-1.983
com	.019	-1.046	-1.114
man	.145	-.337	2.833

Set 1 Linear combination corresponding to unstandardized canonical related variables
variable	1	2	3
led	.007	-.035	-.054
hed	.032	.012	-.005
net	-.002	-.013	.059

Set 2 Linear combination corresponding to unstandardized canonical correlation variables
variable	1	2	3
arti	.029	.030	-.066
com	.001	-.046	-.049
man	.006	-.014	.117

Set 1 typical load
variable	1	2	3
led	.333	-.925	-.185
hed	.993	.101	.057
net	.383	-.753	.535

集合 2 典型载荷
变量	1	2	3
arti	.997	.065	-.043
com	.571	-.811	-.126
man	.922	-.274	.273

集合 1 交叉载荷
变量	1	2	3
led	.331	-.881	-.118
hed	.989	.096	.036
net	.381	-.718	.341

集合 2 交叉载荷
变量	1	2	3
arti	.992	.062	-.028
com	.568	-.773	-.080
man	.918	-.261	.174

已解释的方差比例
典型变量	集合 1 * 自身	集合 1 * 集合 2	集合 2 * 自身	集合 2 * 集合 1
1	.415	.411	.723	.717
2	.478	.434	.246	.223
3	.108	.044	.031	.012