r语言因子分析（Factor analysis of R language）.doc

r语言因子分析(Factor analysis of R language)
Today is to understand what exactly is the factor analysis. Talk nonsense, see the power of R language!
Factor analysis (factor analysis) is the extension and development of ponent analysis, and it is also a dimension reduction method. A class of statistical models for analyzing the role of factors hidden behind surface phenomena. Factor analysis is to study the internal dependence of the correlation matrix or covariance matrix, bines multiple variables into a few factors to reproduce the correlation between the original variables and the factors.
Notice: the hidden factor behind the surface phenomenon
What is an example of "factor analysis
Suppose there are n students with scores of P subjects, using X1, X2,...... Xp represents P subjects, Xi= (Xi1, XI2),...... (XIP), i=1, 2, 3...... N. It is necessary to analyze what factors determine the learning ability of the students who represent the P subjects of the first I students.
All the factors in the subject X have m, such as mathematical derivation factor, memory factor, calculation factor, etc., respectively, denoted as F1, f2,...... FM, i. e.
Xi=ai1*f1+ai2*f2+...... +aim*fm+@, i=1,2,...... P.
With this m unobservable mon factor F1, f2,...... FM (also called a latent factor) and a special factor
@ to describe the original measurable related variables (subjects) X1, X2,...... Xp. And explain and analyze students' learning ability, their coefficient Ai1, ai2,...... AIP is called factor load, which represents the performance of I subjects in M aspects.
The above is the construction of factor model.
In summary, factor analysis is mainly applied in two aspects:
1 for the basic structure, simplified system of observation object would be perplexing relations (variable or sample) integrated into several factors (unobservable random variable), to reproduce the intrinsic link between the factors and the original variables;
For classification, P variables or n samples are cl