CHAPTER 4:
Principal Components Analysis
(主成份分析)
Introduction
研究人员的分析中往往涉及许多变数,要了解这麼多变数的相关型态是非常困难的!这些变数可能有高度相关,使得很多资讯是重复的.也可能导致研重的多元共线性的问题.
主成份分析是一个可以将这些资料重新表达的方法.也就是说主成份分析结果以新的相互不相关的变数取代原有相关之变数,此新的变数为原有变数之线性组合,我们称其为主成份(principal components).
将变数视为多度空间的坐标轴,主成份分析的概念就是对这些座标轴进行旋转(线性组何合)而已.
如果有过多重覆资讯,主成份分析能够将原始资讯浓缩,使分析问题更明确且简易.研究者必须去决定到底要取几个主成份,取得数量愈少愈容易管理分析,而取得数量愈多,就可获得较多的资讯.主成份分析有一个很大的优点,就是它不会有多元共线性的问题.
The first principal component, ξ1, accounts for the maximum variance in the data, the second principal component, ξ2, accounts for the maximum variance that has not been accounted for by the first principal component, and so on.
4.1.1 Potential Applications
Dimension Reduction (资料构面缩减)
Ofir和Simonson在2001年藉著Cacioppo,Petty以及Kao在1984的研究发展出18个问项来评估need for cognition,见表4.1.
TABLE 4.1 Eighteen items used in measuring a survey respondent's "need for cognition"
Item Response
C1 I prefer complex to simple problems.
C2 I like to have the responsibility of handling a situation that requires a lot of thinking.
C3 Thinking is not my idea of fun.(R)
C4 I would rather do something requiring little thought than something that is sure to
challenge my thinking abilities.
C5 I try to anticipate and avoid situations where there is a likely chance that I will have
to think in depth about something.(R)
C6 I find satisfaction in deliberating hard for long hours.
C7 I only think as hard as I have to.(R)
C8 I prefer to think about small daily projects to long-term ones.(R)
C9 I like tasks that require little thought once I've learned them.(R)
C10 The idea of relying on thought to make my way to the top appeals to me.
C11 I really enjoy a task that involves coming up with new solutions to problems.
C12 Learning new ways to think doesn't excite me much.(R)
C13 I prefer my life to be filled with puzzles that I must solve.

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