Factor analysis : healing an ailing model

167 Pages·2013·4.14 MB·English

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 sci-
ences. 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 erro-
Suitbert Ertel
neous 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 Factor Analysis
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 inter- Healing an Ailing Model
relations underlying correlational observations. Ten applications of Varimin (in chpter 2)
show that its results are superior to results obtained by the conventional Varimax proce-
dure. Further applications are presented for sports achievements (chapter 3), intelligence
(chapter 4), and personality (chapter 5). If Varimin keeps on standing the tests new the-
oretical building blocks will arise together with conceptual networks promoting a better
understanding of the domains under study. Readers may check this prognosis by them-
selves using the statistical tool (Varimin) which is provided by open access in the internet.
s
si
y
al
n
A

r
o
t
c
a
F

el
t
r
E

t
r
e
b
t
ui
S

ISBN: 978-3-86395-133-7 Universitätsverlag Göttingen Universitätsverlag Göttingen

Suitbert Ertel
Factor Analysis

This work is licensed under the
Creative Commons License 3.0 “by-sa”,
allowing you to download, distribute and print the
document in a few copies for private or educational
use, given that the document stays unchanged
and the creator is mentioned.
Published in 2013 by Universitätsverlag Göttingen
Suitbert Ertel

Factor Analysis

Healing an Ailing Model

Universitätsverlag Göttingen
2013
Bibliographische Information der Deutschen Nationalbibliothek
Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen
Nationalbibliographie; detaillierte bibliographische Daten sind im Internet über
<http://dnb.ddb.de> abrufbar.

Address of the Author
Suitbert Ertel
e-mail: [email protected]

This work is protected by German Intellectual Property Right Law.
It is also available as an Open Access version through the publisher’s homepage and
the Online Catalogue of the State and University Library of Goettingen
(http://www.sub.uni-goettingen.de). Users of the free online version are invited to
read, download and distribute it.

Set and layout: Franziska Lorenz
Cover: Matthias Bellmann

© 2013 Universitätsverlag Göttingen
http://univerlag.uni-goettingen.de
ISBN: 978-3-86395-133-7
Dedicated to Elisabeth
With Gratitude

Contents
Abbreviations ........................................................................................................... 7
Foreword ................................................................................................................... 9
Preface ..................................................................................................................... 11
Chapter 1 Critique of the simple structure doctrine.................................. 13
Introduction ............................................................................................................ 13
01. The present state of factor analytical research ............................................ 15
02. The doctrine of simple structure (SS) ........................................................... 19
03. The fallacy’s consequences ............................................................................. 21
04. Detailed error analysis ..................................................................................... 23
05. Reorientation .................................................................................................... 27
06. Where did we go wrong? ................................................................................ 32
07. Unheeded critical voices ................................................................................. 34
08. Can non-factorial procedures take us forward? .......................................... 36
4 Contents
Discussion of chapter 1 and outlook ................................................................. 41
Chapter 2 Finding complex structures ......................................................... 43
Introduction ........................................................................................................... 43
Questions and Test Runs ..................................................................................... 45
Test run 1: Evaluating phoneme similarities ..................................................... 49
Test run 2: Similarity judgments of British coins ............................................. 53
Test run 3: Differentiation of response styles at responding to
questionnaires. ....................................................................................................... 59
Test run 4: Semantic features of kinship terms ................................................ 62
Test run 5: Intellectual development in childhood .......................................... 66
Test run 6: Body size and body shape in cattle ................................................. 69
Test run 7: Intelligence tests and performance tests ........................................ 71
Test run 8: Psychophysiological activity indicators (Data: Köhler &). ........ 73
Test run 9: Knowledge test with varying test methods. .................................. 75
Test run 10: Self-assessment and external assessment of children ................ 77
Discussion of chapter 2 ........................................................................................ 79
Chapter 3 Decathlon data under analysis .................................................... 85
Introduction ........................................................................................................... 85
Description of data ............................................................................................... 86
Results: Factor analyses ........................................................................................ 88
1. Interpreting Varimin factors............................................................................ 90
2. Attempt at an interpretation of Varimax factors .......................................... 92
3. Attempt at an interpretation of initial factors ............................................... 94
4. Expert rankings for validating Varimin factors ............................................ 95
Discussion of chapter 3 ........................................................................................ 97
Chapter 4 Intelligence data under analysis ............................................... 101
Study I: Varimin analysis of IST factors .......................................................... 102
Data analysis ......................................................................................................... 104
Results with comments....................................................................................... 105