Principal component analysis and factor analysis
-
The difference between
the principal component analysis by the linear combination of the original variables into a number of principal components integrated
factor analysis by constructing a more specific meaning of several common factors
principal component analysis is a variation of the number of oriented approach
factor analysis of covariance methods is oriented -
Contact
Factor analysis is a generalization of principal component analysis -
Factor analysis of the characteristics of
the number of variable factors is much smaller than the original number of variables
factor is a new integrated variable
no correlation between the factor variable
factors with clear explanatory variables -
Use
reduce the number of variables
by detection of relationships between variables, the original classification variables -
The basic idea of
the higher correlation points in the same class, each class represents a basic structure of
a linear function of the unpredictable few common factors to describe each component of the original observations -
Q-type and R-type Factor Analysis
Factor analysis among samples called Q-type
factor analysis of variance between the type referred to as R
Empirical Analysis eg cement industry operating performance of listed companies Factor Model
d3.10=read.table("clipboard",header = T)
d3.10
X=data.frame(d3.10$x1,d3.10$x2,d3.10$x3,d3.10$x4,d3.10$x5,d3.10$x6)
X
cor(X)
Correlation matrix of the variables to see the relationship between the
next maximum likelihood estimation demand factor loading matrix factanal () function
factanal (X, factors, scores = c ( "none", "regression", "Bartlett"), rotation = "varimax", ...)
X-value matrix or a data frame, the number of factors factor
calculated scores factor scores, including "Regression", "Bartlett"
rotation factor rotation method, default is "varimax"
Fa1=factanal(X,3,rotation = "none")
Fa1$loadings
Load factor loadings correlation coefficients xi and xi represents Fj Fj extent dependent, demanding maximum likelihood estimation of the data, the data must multivariate normal requirements. Consider the method of calculating the principal component
