Session11 - EMSE 171/271 DATA ANALYSIS For Engineers and...

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EMSE 171/271: DATA ANALYSIS For Engineers and Scientists Session 11: Principal Component Analysis (PCA), Introduction, How it works, Mechanics Lecture Notes by: J. René van Dorp 1 www.seas.gwu.edu/~dorpjr 1 Department of Engineering Management and Systems Egineering, School of Engineering and Applied Science, The George Washington University, 1776 G Street, N.W. Suite 110, Washington ß D.C. 20052. E-mail: [email protected]
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EMSE 171/271 - FALL 2005 J.R. van Dorp - 11/11/05; ; Page 235 [email protected] PRINCIPAL COMP. ANAL. Introduction Researchers deal with dozens or even hundreds of variables in their analyses. With that many variables it is difficult to comprehend the patterns of association. This is often complicated by the fact that there is often substantial redundancy among dimensions, leading to high levels of correlation and multicollinearity. Principal component analysis is a method for multivariate data. re-expressing It allows the research to reorient the data so that the first few dimensions account for as much of the available information as possible. The researcher must decide the number of dimensions to use, trading of simplicity for completeness. Each principal component is uncorrelated with all the others and hence captures independent pieces of the information puzzle represented in the larger data set. Providing meaningful interpretation to these principal components is one of the challenges in PCA analysis.
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EMSE 171/271 - FALL 2005 J.R. van Dorp - 11/11/05; ; Page 236 [email protected] PRINCIPAL COMP. ANAL. Dimension Reduction Example application: Creating indices from survey data. Item Response C1 I prefer complex to simple problems C2 I like to have repsonsibility of handling a situation that requires a lot of thinking C3 Thinking is not my idea of fun C4 I would rather do something requiring little though than something that is sure to challenge my thinking abilities C5 I try to antiticipate and avoid situations where there is a little chance that I will have to think in depth about something C6 I find satisfaction in deliberating hard for long hours C7 I only think hard as I have to C8 I prefer to think about small dail projects to long-term ones C9 I like little task that require little though once I have learned them C10 The idea of relying on thought to make my way to the top appeals me C11 I really enjoy a task that involves comin up with new solutions to problems C12 Learning new ways tothink doesn't excite me much C13 I prefer mt life to be filled with puzzles that I must solve C14 The notion of thinking abstractly appeals to me C15 I prefer tasks that are intellectula, difficult, and important to ones that do no require much thought C16 I feel relief rather than satisfaction after completing a taks that required a lot of mental effort C17 It's enough for me that something gets the job done; I don't care how or why it works.
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