Factor analysis
Ertel, Suitbert
Factor analysis

Exploratory factor analysis (EFA) is a statistical tool for digging out hidden factors which give rise to the diversity of manifest objectives in psychology, medicine and other sciences. EFA had its heyday as psychologist Leon Thurstone (1935 and 1948) based EFA on what he called the “principle of simple structure” (SS). This principle, however, was erroneous from the beginning what remained unrecognized despite subsequent inventions of more sophisticated statistical tools such as confirmatory analysis and structural equation modeling. These methods are highly recommended today as tolerable routes to model complexities of observation. But they did not remove the harmful errors that SS had left behind. Five chapters in this book demonstrate and explain the trouble. In chapter 2 the ailment of SS is healed by introducing an unconventional factor rotation, called Varimin. Varimin gives variables of an analysis an optimal opportunity to manifest functional interrelations underlying correlational observations. Ten applications of Varimin (in chapter 2) show that its results are superior to results obtained by the conventional Varimax procedure. Further applications are presented for sports achievements (chapter 3), intelligence (chapter 4), and personality (chapter 5). If Varimin keeps on standing the tests new theoretical building blocks will arise together with conceptual networks promoting a better understanding of the domains under study. Readers may check this prognosis by themselves using the statistical tool (Varimin) which is provided by open access in the internet.

Chapter 1: Critique of the simple structure doctrine
01. The present state of factor analytical research
02. The doctrine of simple structure (SS)
03. The fallacy’s consequences
04. Detailed error analysis
05. Reorientation
06. Where did we go wrong?
07. Unheeded critical voices
08. Can non-factorial procedures take us forward?
Discussion of chapter 1 and outlook
Chapter 2: Finding complex structures
Questions and Test Runs
Test run 1: Evaluating phoneme similarities
Test run 2: Similarity judgments of British coins
Test run 3: Differentiation of response styles at responding to questionnaires
Test run 4: Semantic features of kinship terms
Test run 5: Intellectual development in childhood
Test run 6: Body size and body shape in cattle
Test run 7: Intelligence tests and performance tests
Test run 8: Psychophysiological activity indicators
Test run 9: Knowledge test with varying test methods
Test run 10: Self-assessment and external assessment of children
Discussion of chapter 2
Chapter 3: Decathlon data under analysis
Description of data
Results: Factor analyses
1. Interpreting Varimin factors
2. Attempt at an interpretation of Varimax factors
3. Attempt at an interpretation of initial factors
4. Expert rankings for validating Varimin factors
Discussion of chapter 3
Chapter 4: Intelligence data under analysis
Point of departure and objectives
Study I: Varimin analysis of IST factors
Study II: Validations of Varimin-rotated IST factors
Discussion of chapter 4
Chapter 5: Varimin factors from Big Five personality data
Point of departure
Material and analysis
Towards an interpretation of Varimin factors of personality
More preliminaries
Varimin factor interpretations
Concluding remarks
The interpretations of Varimin factors on probation
Re-interpreting Varimax factors by profiles of Varimin factors
Discussion of chapter 5
Insight and Outlook
Review of chapters 1 to 5
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