danny_liu
一个生产过程有M个变量X_(i),其中每个变量X_(i)抽取n个数据,且服从正态分布(为了简化问题),
其中这M个变量之间是相互联系的(即存在相关系数)。我现在想通过统计方法来寻找出是哪个或哪几个
变量对整个生产过程的影响最大(即变量的方差最大)。
我所用的方法是PCA(主成份分析),PCA是经过线性变化得到新的变量Y,Y_(i)是原变量X_(i)的
一个线性组合。问题就出来,我是相寻找某个或某几个变量的方差最大,但是PCA方法仅提供的是一个线性组合的形式,所以我不知道如何去提出方差最大的几个变量。
请问各位大侠,PCA能解决这个问题吗?或者有什么方法可以解决这个问题呢?
可能我的问题并没有说清楚,请各位感兴趣的大侠,和我联系!
Thanks for your help!
danny_liu
请大侠指点!~
Statsfu
factor analysis is a good method. once you find the first two factors, check the scores of all the variables. the biggest one shows the variable that is most important.
I think so.
danny_liu
TO: Statsfu
I think PCA method is quite same to the factor analysis, is it right?
danny_liu
X_(k)=A_(k)*X_(k)+B_(k-1)*X_(k-1)
其中:X_(k)是第k个变量的数据
A_(k)是第k个变量的误差
B_(k-1)是第k-1个变量的误差
X_(k-1)是第k-1个变量的数据
这个问题的背景是:一个生产过程有M个工序变量X_(i), A_(i)代表X_(i)工序的方差,B_(i-1)代表上一个工序X_(i-1)的方差对这一工序X_(i)的方差。
这个模型算不算回归模型呢?这样建立模型有问题吗?如果这样建立是可行的话,如何去估计这个模型的参数呢?
anita_jiu
To Danny Liu
PCA and FA are not quite the same. They are two different techniques and work on different purposes and analytical approaches, although quite often, they would produce similar results. One fundamental difference in relation to analysis purpose is that PCA is often recommended for data reduction while FA is to detect the underlying structure of the variables.
Also, FA works on a mathematical model and factors may be estimated. On the other hand, PCA simply transforms your original variables into a new set of linear combinations (that's why they called the principal components) (Stevens, 1992: p375).
If you may get hold of this book [by Tabachnick, B. G. and Fidell, L. S. (1989), Using Multivariate Statistics (2nd), Harper Collins Publishers, U.S.A ], you may learn more about these two techniques. Good luck.
pigtail
是否可以考虑用偏最小二乘法呢