MASON PSYC 612 - Lecture 1: Principal Components Analysis

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PSYC 612, SPRING 2012Lecture 1: Principal Components Analysis (PCA)Lecture Date: 1/26/2012Contents1 Preliminary Questions 12 Part I: Introduction (20 minutes; 2 minute break) 22.1 An Advance Organizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Learning Assumptions and Framework . . . . . . . . . . . . . . . . . . . . . . . . . 23 Part II: Review Dunteman; pages 5-42 (50 minutes; 5 minute break) 33.1 Purpose: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.2 Objectives: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.3 PCA Introduction and Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.3.1 PCA application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.3.2 Data Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.3.3 PCA Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.3.4 PCA Example Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.3.5 MRC Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.3.6 Another PCA Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.4 Dunteman Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 Part III: Important points about PCA not covered in the reading 184.1 Purpose: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.2 Objectives: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.3 PCA assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.4 Components and factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Preliminary Questions• Have you read all the assigned reading for today (Dunteman)?• Did you understand the material?• Do you understand the process of the modules?12 Part I: Introduction (20 minutes; 2 minute break)2.1 An Advance OrganizerV1V2V3AV4V5V6CV1V2V3AV4V5V6CV1V2V3AV4V5V6C2.2 Learning Assumptions and FrameworkBeginBasic ArithmeticSimple CalculationsConceptual UnderstandingPrincipled Application23 Part II: Review Dunteman; pages 5-42 (50 minutes; 5minute break)3.1 Purpose:To review the first half of the assigned reading3.2 Objectives:1. Introduce the PCA procedure and put that procedure into the context of data analysis2. Review material as presented by Dunteman by highlighting the important points3.3 PCA Introduction and ExampleI begin our discussion of PCA with an example from sports - the women’s heptathlon. The hep-tathlon is a seven event competition consisting of the 100m hurdles (hurdles), high jump (highjump),shot put (shot), 200m run (run200m), long jump (longjump), javelin throw (javelin), and 800m run(run800m).Each event is scored according to a complex system of rankings between individual competitorsand weights according to the performance. For example, a competitor who runs the fastest 100mhurdles and does it in record time would gain more points than just winning the event. The datasetabove shows the results from the 1988 event held during the Olympics in Seoul, Korea. We mightwonder how these events may be grouped into logical sets that tells us something about the scoring.Those event groupings may tell us something about how the athletes compare to one another aswell. Strength, for example, is a primary concern in the shot put and javelin throw whereas speedis more of a concern in the 100m hurdles and 200m running races.3.3.1 PCA applicationThe “discovery”of variable groups can be done with a variety of statistical tools; one tool is principalcomponents analysis or PCA. Heptathlon data serve our purposes perfectly for this statistical tool.We have a collection of sporting events completed by each person that share some common elementsand unique elements. Apologies to those who dislike sports and sports data but I assure you thatthis is an example that will make sense without much trouble on your part; you do not even needto know about the event to appreciate the example. Let me describe the events first.3hurdles highjump shot run200m longjump javelin run800m scoreJoyner-Kersee (USA) 12.69 1.86 15.80 22.56 7.27 45.66 128.51 7291John (GDR) 12.85 1.80 16.23 23.65 6.71 42.56 126.12 6897Behmer (GDR) 13.20 1.83 14.20 23.10 6.68 44.54 124.20 6858Sablovskaite (URS) 13.61 1.80 15.23 23.92 6.25 42.78 132.24 6540Choubenkova (URS) 13.51 1.74 14.76 23.93 6.32 47.46 127.90 6540Schulz (GDR) 13.75 1.83 13.50 24.65 6.33 42.82 125.79 6411Fleming (AUS) 13.38 1.80 12.88 23.59 6.37 40.28 132.54 6351Greiner (USA) 13.55 1.80 14.13 24.48 6.47 38.00 133.65 6297Lajbnerova (CZE) 13.63 1.83 14.28 24.86 6.11 42.20 136.05 6252Bouraga (URS) 13.25 1.77 12.62 23.59 6.28 39.06 134.74 6252Wijnsma (HOL) 13.75 1.86 13.01 25.03 6.34 37.86 131.49 6205Dimitrova (BUL) 13.24 1.80 12.88 23.59 6.37 40.28 132.54 6171Scheider (SWI) 13.85 1.86 11.58 24.87 6.05 47.50 134.93 6137Braun (FRG) 13.71 1.83 13.16 24.78 6.12 44.58 142.82 6109Ruotsalainen (FIN) 13.79 1.80 12.32 24.61 6.08 45.44 137.06 6101Yuping (CHN) 13.93 1.86 14.21 25.00 6.40 38.60 146.67 6087Hagger (GB) 13.47 1.80 12.75 25.47 6.34 35.76 138.48 5975Brown (USA) 14.07 1.83 12.69 24.83 6.13 44.34 146.43 5972Mulliner (GB) 14.39 1.71 12.68 24.92 6.10 37.76 138.02 5746Hautenauve (BEL) 14.04 1.77 11.81 25.61 5.99 35.68 133.90 5734Kytola (FIN) 14.31 1.77 11.66 25.69 5.75 39.48 133.35 5686Geremias (BRA) …


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