15. Principal Component Analysis

Introduction: The Basics of Principal Component Analysis430
 A Variable Reduction Procedure430
 An Illustration of Variable Redundancy431
 What Is a Principal Component?433
 Principal Component Analysis Is Not Factor Analysis436
Example: Analysis of the Prosocial Orientation Inventory438
 Preparing a Multiple-Item Instrument439
 Number of Items per Component439
 Minimally Adequate Sample Size440
SAS Program and Output441
 Writing the SAS Program441
 Results from the Output444
Steps in Conducting Principal Component Analysis449
 Step 1: Initial Extraction of the Components449
 Step 2: Determining How Many “Meaningful” Components to Retain449
 Step 3: Rotation to a Final Solution455
 Step 4: Interpreting the Rotated Solution456
 Step 5: Creating Factor Scores or Factor-Based Scores458
 Step 6: Summarizing the Results in a Table466
 Step 7: Preparing a Formal Description of the Results for a Paper468
An Example with Three Retained Components468
 The Questionnaire468
 Writing the Program470
 Results of the Initial Analysis471
 Results of the Second Analysis477
Conclusion481
Assumptions Underlying Principal Component Analysis481
References481

Overview

This chapter provides an introduction to principal component analysis: a variable-reduction procedure similar to factor analysis. The chapter provides guidelines regarding the necessary sample size and number of items per component. It shows how to determine the number of components to retain, interpret the rotated solution, create factor scores, and summarize the results. Fictitious data from two studies are analyzed to illustrate these procedures. The present chapter deals only with the creation of orthogonal (uncorrelated) components.


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