Understanding correlation matrices:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Los Angeles ; London ; New Delhi ; Singapore ; Washington DC ; Melbourne
SAGE
[2021]
|
| Series: | Quantitative applications in the social sciences
186 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | xviii, 118 Seiten Diagramme |
| ISBN: | 9781544341095 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Understanding
Correlation Matrices
Alexandria Hadd
Spelman College
Joseph Lee Rodgers
Vanderbilt University
Quantitative Applications in the Social Sciences, Volume 186
®SAGE
Los Angeles 1 London | New Delhl
Singapore lwwdngton DC I Melbourne
TABLE OF CONTENTS
Series Editors Introduction xi
Preface xiii
Acknowledgments xv
About the Authors xvii
Chapter 1: Introduction 1
The Correlation Coefficient: A Conceptual Introduction 2
The Covariance 3
The Correlation Coefficient and Linear Algebra:
Brief Histories 5
Examples of Correlation Matrices 8
Summary 15
Chapter 2: The Mathematics of Correlation Matrices 17
Requirements of Correlation Matrices 18
Eigenvalues of a Correlation Matrix 20
Pseudo—Correlation Matrices and Positive Definite Matrices 21
Smoothing Techniques 23
Restriction of Correlation Ranges in the Matrix 25
The Inverse of a Correlation Matrix 25
The Determinant of a Correlation Matrix 26
Examples 27
Racial Composition of NBA and Sponsor Cities 27
Girls Intelligence Across Development 27
Summary 28
Chaliter 3: Statistical Hypothesis Testing on Correlation Matrices 29
Hypotheses About Correlations in a Single Correlation Matrix 30
Testing Equality of 71420 Correlations in a Correlation
Matrix (No Variable in Common) 30
Testing Equality of Two Correlations in a Correlation
Matrix (Variable in Common) 32
Testing Equality to a Specified Population Correlation
Matrix I
Hypotheses About Two or More Correlatlon Matrices
Testing Equality ofTwo Correlation Matrices From
Independent Groups
Testing Equality of Several Correlation Matrices
Testing Equality of Several Correlations From
Independent Samples
Testing for Linear Trend of Eigenvalues
Summary
Chapter 4: Methods for Correlation/Covariance
Matrices as the Input Data
Factor Analysis
Summary
Example
Resources fiJr Software and Additional Readings
Structural Equation Modeling
Summary
Examples
Resources for Software and Additional Readings
Meta—Analysis of Correlation Matrices
Summary
Recent MASEM Examples
Resources for Software and Additional Readings
Summary
Chapter 5: Graphing Correlation Matrices
Graphing Correlations
Graphing Correlation Matrices
The Scatterplot Matrix
The Scatterplot Matrix, Enhanced
Corrgrams Using the corrplot Package in R
Heat Maps
Parallel Coordinate Plots
Eigenvector Plots
Summary
Chapter 6: The Geometry of Correlation Matrices
What Is Correlation Space?
The 3x3 Correlation Space
Properties of Correlation Space: The Shape and Size
Convexity of the Space
Number of Vertices and Edges
Volume Relative to Space of Pseudo-Correlations
Uses of Correlation Space
Similarity of Correlation Matrices
Generating Random Correlation Matrices
Fungible Correlation Matrices
Defining Correlation Spaces Using Angles
Example Using 3X3 and 4X4 Correlation Space
Summary
Chapter 7: Conclusion
References
Index
|
| adam_txt |
Understanding
Correlation Matrices
Alexandria Hadd
Spelman College
Joseph Lee Rodgers
Vanderbilt University
Quantitative Applications in the Social Sciences, Volume 186
®SAGE
Los Angeles 1 London | New Delhl
Singapore lwwdngton DC I Melbourne
TABLE OF CONTENTS
Series Editors Introduction xi
Preface xiii
Acknowledgments xv
About the Authors xvii
Chapter 1: Introduction 1
The Correlation Coefficient: A Conceptual Introduction 2
The Covariance 3
The Correlation Coefficient and Linear Algebra:
Brief Histories 5
Examples of Correlation Matrices 8
Summary 15
Chapter 2: The Mathematics of Correlation Matrices 17
Requirements of Correlation Matrices 18
Eigenvalues of a Correlation Matrix 20
Pseudo—Correlation Matrices and Positive Definite Matrices 21
Smoothing Techniques 23
Restriction of Correlation Ranges in the Matrix 25
The Inverse of a Correlation Matrix 25
The Determinant of a Correlation Matrix 26
Examples 27
Racial Composition of NBA and Sponsor Cities 27
Girls ' Intelligence Across Development 27
Summary 28
Chaliter 3: Statistical Hypothesis Testing on Correlation Matrices 29
Hypotheses About Correlations in a Single Correlation Matrix 30
Testing Equality of 71420 Correlations in a Correlation
Matrix (No Variable in Common) 30
Testing Equality of Two Correlations in a Correlation
Matrix (Variable in Common) 32
Testing Equality to a Specified Population Correlation
Matrix ' I
Hypotheses About Two or More Correlatlon Matrices
Testing Equality ofTwo Correlation Matrices From
Independent Groups
Testing Equality of Several Correlation Matrices
Testing Equality of Several Correlations From
Independent Samples
Testing for Linear Trend of Eigenvalues
Summary
Chapter 4: Methods for Correlation/Covariance
Matrices as the Input Data
Factor Analysis
Summary
Example
Resources fiJr Software and Additional Readings
Structural Equation Modeling
Summary
Examples
Resources for Software and Additional Readings
Meta—Analysis of Correlation Matrices
Summary
Recent MASEM Examples
Resources for Software and Additional Readings
Summary
Chapter 5: Graphing Correlation Matrices
Graphing Correlations
Graphing Correlation Matrices
The Scatterplot Matrix
The Scatterplot Matrix, Enhanced
Corrgrams Using the corrplot Package in R
Heat Maps
Parallel Coordinate Plots
Eigenvector Plots
Summary
Chapter 6: The Geometry of Correlation Matrices
What Is Correlation Space?
The 3x3 Correlation Space
Properties of Correlation Space: The Shape and Size
Convexity of the Space
Number of Vertices and Edges
Volume Relative to Space of Pseudo-Correlations
Uses of Correlation Space
Similarity of Correlation Matrices
Generating Random Correlation Matrices
Fungible Correlation Matrices
Defining Correlation Spaces Using Angles
Example Using 3X3 and 4X4 Correlation Space
Summary
Chapter 7: Conclusion
References
Index |
| any_adam_object | 1 |
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| ctrlnum | (OCoLC)1238102462 (DE-599)KXP1726208052 |
| discipline | Soziologie |
| discipline_str_mv | Soziologie |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T16:53:02Z |
| indexdate | 2024-07-10T09:05:39Z |
| institution | BVB |
| isbn | 9781544341095 |
| language | English |
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| publishDateSearch | 2021 |
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| series | Quantitative applications in the social sciences |
| series2 | Quantitative applications in the social sciences |
| spelling | Hadd, Alexandria (DE-588)1229932488 aut Understanding correlation matrices Alexandria Hadd, Spelman College, Joseph Lee Rodgers, Vanderbilt University Los Angeles ; London ; New Delhi ; Singapore ; Washington DC ; Melbourne SAGE [2021] xviii, 118 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Quantitative applications in the social sciences 186 Korrelation (DE-588)4165343-9 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Korrelation (DE-588)4165343-9 s Matrix Mathematik (DE-588)4037968-1 s DE-604 Rodgers, Joseph Lee 1953- (DE-588)1221087509 aut Erscheint auch als Online-Ausgabe, epub 978-1-5443-4107-1 Erscheint auch als Online-Ausgabe, epub 978-1-5443-4108-8 Erscheint auch als Online-Ausgabe, ePDF 978-1-5443-4110-1 Quantitative applications in the social sciences 186 (DE-604)BV000005102 186 V:DE-605;X:semantics application/pdf http://digitale-objekte.hbz-nrw.de/storage2/2021/03/17/file_1/9008324.pdf Inhaltsverzeichnis HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032612313&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hadd, Alexandria Rodgers, Joseph Lee 1953- Understanding correlation matrices Quantitative applications in the social sciences Korrelation (DE-588)4165343-9 gnd Matrix Mathematik (DE-588)4037968-1 gnd |
| subject_GND | (DE-588)4165343-9 (DE-588)4037968-1 |
| title | Understanding correlation matrices |
| title_auth | Understanding correlation matrices |
| title_exact_search | Understanding correlation matrices |
| title_exact_search_txtP | Understanding correlation matrices |
| title_full | Understanding correlation matrices Alexandria Hadd, Spelman College, Joseph Lee Rodgers, Vanderbilt University |
| title_fullStr | Understanding correlation matrices Alexandria Hadd, Spelman College, Joseph Lee Rodgers, Vanderbilt University |
| title_full_unstemmed | Understanding correlation matrices Alexandria Hadd, Spelman College, Joseph Lee Rodgers, Vanderbilt University |
| title_short | Understanding correlation matrices |
| title_sort | understanding correlation matrices |
| topic | Korrelation (DE-588)4165343-9 gnd Matrix Mathematik (DE-588)4037968-1 gnd |
| topic_facet | Korrelation Matrix Mathematik |
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| volume_link | (DE-604)BV000005102 |
| work_keys_str_mv | AT haddalexandria understandingcorrelationmatrices AT rodgersjosephlee understandingcorrelationmatrices |
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