An introduction to applied multivariate analysis:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Routledge
2008
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 485 S. |
| ISBN: | 0805863753 9780805863758 |
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| 100 | 1 | |a Raykov, Tenko |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to applied multivariate analysis |c Tenko Raykov ; George A. Marcoulides |
| 264 | 1 | |a New York [u.a.] |b Routledge |c 2008 | |
| 300 | |a X, 485 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Multivariate analyse |2 gtt | |
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| adam_text | Contents
Preface
.
їх
Chapter
1
Introduction to Multivariate Statistics
1.1
Definition of Multivariate Statistics
.............................................1
1.2
Relationship of Multivariate Statistics
to Univariate Statistics
..................................................................5
1.3
Choice of Variables and Multivariate Method,
and the Concept of Optimal Linear Combination
.......................7
1.4
Data for Multivariate Analyses
....................................................8
1.5
Three Fundamental Matrices in Multivariate Statistics
............11
1.5.1
Covariance Matrix
......................................................................12
1.5.2
Correlation Matrix
......................................................................13
1.5.3
Sums-of-Squares and Cross-Products Matrix
........................15
1.6
Illustration Using Statistical Software
........................................17
Chapter
2
Elements of Matrix Theory
2.1
Matrix Definition
.........................................................................31
2.2
Matrix Operations, Determinant, and Trace
..............................33
2.3
Using SPSS and
SAS
for Matrix Operations
..............................46
2.4
General Form of Matrix Multiplications With Vector,
and Representation of the Covariance, Correlation,
and Sum-of-Squares and Cross-Product Matrices
.....................50
2.4.1
Linear Modeling and Matrix Multiplication
..........................50
2.4.2
Three Fundamental Matrices of Multivariate Statistics
in Compact Form
.......................................................................51
2.5
Raw Data Points in Higher Dimensions, and Distance
Between Them
..............................................................................54
Chapter
3
Data Screening and Preliminary Analyses
3.1
Initial Data Exploration
...............................................................61
3.2
Outliers and the Search for Them
...............................................69
3.2.1
Univariate Outliers
.....................................................................69
3.2.2
Multivariate Outliers
.................................................................71
3.2.3
Handling Outliers: A Revisit
....................................................78
3.3
Checking of Variable Distribution Assumptions
.......................80
3.4
Variable Transformations
............................................................83
HI
IV
Chapter
4
Multivariate Analysis of Group Differences
4.1
A Start-Up Example
....................................................................99
4.2
A Definition of the Multivariate Normal Distribution
............101
4.3
Testing Hypotheses About a Multivariate Mean
.....................102
4.3.1
The Case of Known Covariance Matrix
................................103
4.3.2
The Case of Unknown Covariance Matrix
...........................107
4.4
Testing Hypotheses About Multivariate Means of
Two Groups
...............................................................................110
4.4.1
Two Related or Matched Samples
(Change Over Time)
................................................................110
4.4.2
Two Unrelated (Independent) Samples
................................113
4.5
Testing Hypotheses About Multivariate Means
in One-Way and Higher Order Designs (Multivariate
Analysis of Variance,
MÁNOVA)
.............................................116
4.5.1
Statistical Significance Versus Practical Importance
...........129
4.5.2
Higher Order
MÁNOVA
Designs
.........................................130
4.5.3
Other Test Criteria
...................................................................132
4.6
MÁNOVA
Follow-Up Analyses
...............................................143
4.7
Limitations and Assumptions of
MÁNOVA
............................145
Chapter
5
Repeated Measure Analysis of Variance
5.1
Between-Subject and Within-Subject Factors
and Designs
................................................................................148
5.2
Univariate Approach to Repeated Measure Analysis
.............150
5.3
Multivariate Approach to Repeated Measure Analysis
..........168
5.4
Comparison of Univariate and Multivariate Approaches
to Repeated Measure Analysis
..................................................179
Chapter
6
Analysis of Covariance
6.1
Logic of Analysis of Covariance
...............................................182
6.2
Multivariate Analysis of Covariance
........................................192
6.3
Step-Down Analysis (Roy-Bargmann Analysis)
.....................198
6.4
Assumptions of Analysis of Covariance
..................................203
Chapter
7
Principal Component Analysis
7.1
Introduction
...............................................................................211
7.2
Beginnings of Principal Component Analysis
.........................213
7.3
How Does Principal Component Analysis Proceed?
...............220
7.4
Illustrations of Principal Component Analysis
.......................224
7.4.1
Analysis of the Covariance Matrix X (S) of the
Original Variables
....................................................................224
7.4.2
Analysis of the Correlation Matrix
Ρ (Κ)
of the
Original Variables
....................................................................224
7.5
Using Principal Component Analysis in Empirical Research
.........234
7.5.1
Multicollinearity Detection
.....................................................234
7.5.2
PCA
With Nearly Uncorrelated Variables Is
Meaningless
...............................................................................235
7.5.3
Can PCA Be Used as a Method for Observed Variable
Elimination?
..............................................................................236
7.5.4
Which Matrix Should Be Analyzed?
.....................................236
7.5.5
PCA as a Helpful Aid in Assessing Multinormality
..........237
7.5.6
PCA as Orthogonal Regression
.........................................237
7.5.7
PCA Is Conducted via Factor Analysis Routines in
Some Software
..........................................................................237
7.5.8
PCA as a Rotation of Original Coordinate Axes
.................238
7.5.9
PCA as a Data Exploratory Technique
.................................238
Chapter
8
Exploratory Factor Analysis
8.1
Introduction
...............................................................................241
8.2
Model of Factor Analysis
..........................................................242
8.3
How Does Factor Analysis Proceed?
........................................248
8.3.1
Factor Extraction
......................................................................248
8.3.1.1
Principal Component Method
.................................248
8.3.1.2
Maximum Likelihood Factor Analysis
...................256
8.3.2
Factor Rotation
.........................................................................262
8.3.2.1
Orthogonal Rotation
.................................................266
8.3.2.2
Oblique Rotation
.......................................................267
8.4
Heywood Cases
.........................................................................273
8.5
Factor Score Estimation
.............................................................273
8.5.1
Weighted Least Squares Method
(Generalized Least Squares Method)
....................................274
8.5.2
Regression Method
..................................................................274
8.6
Comparison of Factor Analysis and Principal
Component Analysis
.................................................................276
Chapter
9
Confirmatory Factor Analysis
9.1
Introduction
...............................................................................279
9.2
A Start-Up Example
..................................................................279
9.3
Confirmatory Factor Analysis Model
.......................................281
9.4
Fitting Confirmatory Factor Analysis Models
.........................284
9.5
A Brief Introduction to Mplus, and Fitting the
Example Model
.........................................................................................287
9.6
Testing Parameter Restrictions in Confirmatory Factor
Analysis Models
........................................................................298
9.7
Specification Search and Model Fit Improvement
...................300
9.8
Fitting Confirmatory Factor Analysis Models to the
Mean and Covariance Structure
...............................................307
9.9
Examining Group Differences on Latent Variables
.................314
VI
Chapter
10
Discriminant Function Analysis
10.1
Introduction
.............................................................................331
10.2
What Is Discriminant Function Analysis?
..............................332
10.3
Relationship of Discriminant Function Analysis to Other
Multivariate Statistical Methods
.............................................334
10.4
Discriminant Function Analysis With Two Groups
..............336
10.5
Relationship Between Discriminant Function and
Regression Analysis With Two Groups
.................................351
10.6
Discriminant Function Analysis With More Than
Two Groups
.............................................................................353
10.7
Tests in Discriminant Function Analysis
...............................355
10.8
Limitations of Discriminant Function Analysis
.....................364
Chapter
11
Canonical Correlation Analysis
11.1
Introduction
.............................................................................367
11.2
How Does Canonical Correlation Analysis Proceed?
...........370
11.3
Tests and Interpretation of Canonical
Variâtes
.....................372
11.4
Canonical Correlation Approach to Discriminant
Analysis
....................................................................................384
11.5
Generality of Canonical Correlation Analysis
.......................389
Chapter
12
An Introduction to the Analysis
of Missing Data
12.1
Goals of Missing Data Analysis
..............................................391
12.2
Patterns of Missing Data
.........................................................392
12.3
Mechanisms of Missing Data
..................................................394
12.3.1
Missing Completely at Random
........................................396
12.3.2
Missing at Random
..............................................................398
12.3.3
Ignorable
Missingness and Nonignorable
Missingness Mechanisms
....................................................400
12.4
Traditional Ways of Dealing With Missing Data
...................401
12.4.1
Listwise Deletion
..................................................................402
12.4.2
Pairwise Deletion
.................................................................402
12.4.3
Dummy Variable Adjustment
............................................403
12.4.4
Simple Imputation Methods
...............................................403
12.4.5
Weighting Methods
.............................................................405
12.5
Full Information Maximum Likelihood
and Multiple Imputation
.........................................................406
12.6
Examining Group Differences and Similarities
in the Presence of Missing Data
...............................................407
12.6.1
Examining Group Mean Differences With
Incomplete Data
...................................................................410
12.6.2
Testing for Group Differences in the Covariance
and Correlation Matrices With Missing Data
..................427
Vil
Chapter
13
Multivariate
Analysis of Change Processes
13.1
Introduction
.............................................................................433
13.2
Modeling Change Over Time With Time-Invariant
and Time-Varying Covariates
.................................................434
13.2.1
Intercept-and-Slope Model
.................................................435
13.2.2
Inclusion of Time-Varying and Time-Invariant
Covariates
..............................................................................436
13.2.3
An Example Application
.....................................................437
13.2.4
Testing Parameter Restrictions
...........................................442
13.3
Modeling General Forms of Change Over Time
.....................448
13.3.1
Level-and-Shape Model
.......................................................448
13.3.2
Empirical Illustration
...........................................................450
13.3.3
Testing Special Patterns of Growth or Decline
................455
13.3.4
Possible Causes of Inadmissible Solutions
.......................459
13.4
Modeling Change Over Time With Incomplete Data
............461
Appendix: Variable Naming and Order for Data Files
............467
References
..........................................................................................469
Author Index
.....................................................................................473
Subject Index
.....................................................................................477
|
| adam_txt |
Contents
Preface
.
їх
Chapter
1
Introduction to Multivariate Statistics
1.1
Definition of Multivariate Statistics
.1
1.2
Relationship of Multivariate Statistics
to Univariate Statistics
.5
1.3
Choice of Variables and Multivariate Method,
and the Concept of Optimal Linear Combination
.7
1.4
Data for Multivariate Analyses
.8
1.5
Three Fundamental Matrices in Multivariate Statistics
.11
1.5.1
Covariance Matrix
.12
1.5.2
Correlation Matrix
.13
1.5.3
Sums-of-Squares and Cross-Products Matrix
.15
1.6
Illustration Using Statistical Software
.17
Chapter
2
Elements of Matrix Theory
2.1
Matrix Definition
.31
2.2
Matrix Operations, Determinant, and Trace
.33
2.3
Using SPSS and
SAS
for Matrix Operations
.46
2.4
General Form of Matrix Multiplications With Vector,
and Representation of the Covariance, Correlation,
and Sum-of-Squares and Cross-Product Matrices
.50
2.4.1
Linear Modeling and Matrix Multiplication
.50
2.4.2
Three Fundamental Matrices of Multivariate Statistics
in Compact Form
.51
2.5
Raw Data Points in Higher Dimensions, and Distance
Between Them
.54
Chapter
3
Data Screening and Preliminary Analyses
3.1
Initial Data Exploration
.61
3.2
Outliers and the Search for Them
.69
3.2.1
Univariate Outliers
.69
3.2.2
Multivariate Outliers
.71
3.2.3
Handling Outliers: A Revisit
.78
3.3
Checking of Variable Distribution Assumptions
.80
3.4
Variable Transformations
.83
HI
IV
Chapter
4
Multivariate Analysis of Group Differences
4.1
A Start-Up Example
.99
4.2
A Definition of the Multivariate Normal Distribution
.101
4.3
Testing Hypotheses About a Multivariate Mean
.102
4.3.1
The Case of Known Covariance Matrix
.103
4.3.2
The Case of Unknown Covariance Matrix
.107
4.4
Testing Hypotheses About Multivariate Means of
Two Groups
.110
4.4.1
Two Related or Matched Samples
(Change Over Time)
.110
4.4.2
Two Unrelated (Independent) Samples
.113
4.5
Testing Hypotheses About Multivariate Means
in One-Way and Higher Order Designs (Multivariate
Analysis of Variance,
MÁNOVA)
.116
4.5.1
Statistical Significance Versus Practical Importance
.129
4.5.2
Higher Order
MÁNOVA
Designs
.130
4.5.3
Other Test Criteria
.132
4.6
MÁNOVA
Follow-Up Analyses
.143
4.7
Limitations and Assumptions of
MÁNOVA
.145
Chapter
5
Repeated Measure Analysis of Variance
5.1
Between-Subject and Within-Subject Factors
and Designs
.148
5.2
Univariate Approach to Repeated Measure Analysis
.150
5.3
Multivariate Approach to Repeated Measure Analysis
.168
5.4
Comparison of Univariate and Multivariate Approaches
to Repeated Measure Analysis
.179
Chapter
6
Analysis of Covariance
6.1
Logic of Analysis of Covariance
.182
6.2
Multivariate Analysis of Covariance
.192
6.3
Step-Down Analysis (Roy-Bargmann Analysis)
.198
6.4
Assumptions of Analysis of Covariance
.203
Chapter
7
Principal Component Analysis
7.1
Introduction
.211
7.2
Beginnings of Principal Component Analysis
.213
7.3
How Does Principal Component Analysis Proceed?
.220
7.4
Illustrations of Principal Component Analysis
.224
7.4.1
Analysis of the Covariance Matrix X (S) of the
Original Variables
.224
7.4.2
Analysis of the Correlation Matrix
Ρ (Κ)
of the
Original Variables
.224
7.5
Using Principal Component Analysis in Empirical Research
.234
7.5.1
Multicollinearity Detection
.234
7.5.2
PCA
With Nearly Uncorrelated Variables Is
Meaningless
.235
7.5.3
Can PCA Be Used as a Method for Observed Variable
Elimination?
.236
7.5.4
Which Matrix Should Be Analyzed?
.236
7.5.5
PCA as a Helpful Aid in Assessing Multinormality
.237
7.5.6
PCA as "Orthogonal" Regression
.237
7.5.7
PCA Is Conducted via Factor Analysis Routines in
Some Software
.237
7.5.8
PCA as a Rotation of Original Coordinate Axes
.238
7.5.9
PCA as a Data Exploratory Technique
.238
Chapter
8
Exploratory Factor Analysis
8.1
Introduction
.241
8.2
Model of Factor Analysis
.242
8.3
How Does Factor Analysis Proceed?
.248
8.3.1
Factor Extraction
.248
8.3.1.1
Principal Component Method
.248
8.3.1.2
Maximum Likelihood Factor Analysis
.256
8.3.2
Factor Rotation
.262
8.3.2.1
Orthogonal Rotation
.266
8.3.2.2
Oblique Rotation
.267
8.4
Heywood Cases
.273
8.5
Factor Score Estimation
.273
8.5.1
Weighted Least Squares Method
(Generalized Least Squares Method)
.274
8.5.2
Regression Method
.274
8.6
Comparison of Factor Analysis and Principal
Component Analysis
.276
Chapter
9
Confirmatory Factor Analysis
9.1
Introduction
.279
9.2
A Start-Up Example
.279
9.3
Confirmatory Factor Analysis Model
.281
9.4
Fitting Confirmatory Factor Analysis Models
.284
9.5
A Brief Introduction to Mplus, and Fitting the
Example Model
.287
9.6
Testing Parameter Restrictions in Confirmatory Factor
Analysis Models
.298
9.7
Specification Search and Model Fit Improvement
.300
9.8
Fitting Confirmatory Factor Analysis Models to the
Mean and Covariance Structure
.307
9.9
Examining Group Differences on Latent Variables
.314
VI
Chapter
10
Discriminant Function Analysis
10.1
Introduction
.331
10.2
What Is Discriminant Function Analysis?
.332
10.3
Relationship of Discriminant Function Analysis to Other
Multivariate Statistical Methods
.334
10.4
Discriminant Function Analysis With Two Groups
.336
10.5
Relationship Between Discriminant Function and
Regression Analysis With Two Groups
.351
10.6
Discriminant Function Analysis With More Than
Two Groups
.353
10.7
Tests in Discriminant Function Analysis
.355
10.8
Limitations of Discriminant Function Analysis
.364
Chapter
11
Canonical Correlation Analysis
11.1
Introduction
.367
11.2
How Does Canonical Correlation Analysis Proceed?
.370
11.3
Tests and Interpretation of Canonical
Variâtes
.372
11.4
Canonical Correlation Approach to Discriminant
Analysis
.384
11.5
Generality of Canonical Correlation Analysis
.389
Chapter
12
An Introduction to the Analysis
of Missing Data
12.1
Goals of Missing Data Analysis
.391
12.2
Patterns of Missing Data
.392
12.3
Mechanisms of Missing Data
.394
12.3.1
Missing Completely at Random
.396
12.3.2
Missing at Random
.398
12.3.3
Ignorable
Missingness and Nonignorable
Missingness Mechanisms
.400
12.4
Traditional Ways of Dealing With Missing Data
.401
12.4.1
Listwise Deletion
.402
12.4.2
Pairwise Deletion
.402
12.4.3
Dummy Variable Adjustment
.403
12.4.4
Simple Imputation Methods
.403
12.4.5
Weighting Methods
.405
12.5
Full Information Maximum Likelihood
and Multiple Imputation
.406
12.6
Examining Group Differences and Similarities
in the Presence of Missing Data
.407
12.6.1
Examining Group Mean Differences With
Incomplete Data
.410
12.6.2
Testing for Group Differences in the Covariance
and Correlation Matrices With Missing Data
.427
Vil
Chapter
13
Multivariate
Analysis of Change Processes
13.1
Introduction
.433
13.2
Modeling Change Over Time With Time-Invariant
and Time-Varying Covariates
.434
13.2.1
Intercept-and-Slope Model
.435
13.2.2
Inclusion of Time-Varying and Time-Invariant
Covariates
.436
13.2.3
An Example Application
.437
13.2.4
Testing Parameter Restrictions
.442
13.3
Modeling General Forms of Change Over Time
.448
13.3.1
Level-and-Shape Model
.448
13.3.2
Empirical Illustration
.450
13.3.3
Testing Special Patterns of Growth or Decline
.455
13.3.4
Possible Causes of Inadmissible Solutions
.459
13.4
Modeling Change Over Time With Incomplete Data
.461
Appendix: Variable Naming and Order for Data Files
.467
References
.469
Author Index
.473
Subject Index
.477 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Raykov, Tenko Marcoulides, George A. 1955- |
| author_GND | (DE-588)171190467 |
| author_facet | Raykov, Tenko Marcoulides, George A. 1955- |
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| author_sort | Raykov, Tenko |
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| ctrlnum | (OCoLC)173368697 (DE-599)BVBBV023410665 |
| dewey-full | 519.5/35 519.535 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-search | 519.5/35 519.535 |
| dewey-sort | 3519.5 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Soziologie Psychologie Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Soziologie Psychologie Mathematik Wirtschaftswissenschaften |
| format | Book |
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| genre | (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV023410665 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:27:24Z |
| indexdate | 2025-02-20T06:37:48Z |
| institution | BVB |
| isbn | 0805863753 9780805863758 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016593280 |
| oclc_num | 173368697 |
| open_access_boolean | |
| owner | DE-703 DE-19 DE-BY-UBM DE-29 DE-739 DE-11 DE-91 DE-BY-TUM DE-188 DE-862 DE-BY-FWS |
| owner_facet | DE-703 DE-19 DE-BY-UBM DE-29 DE-739 DE-11 DE-91 DE-BY-TUM DE-188 DE-862 DE-BY-FWS |
| physical | X, 485 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Routledge |
| record_format | marc |
| spellingShingle | Raykov, Tenko Marcoulides, George A. 1955- An introduction to applied multivariate analysis Multivariate analyse gtt Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd |
| subject_GND | (DE-588)4040708-1 (DE-588)4151278-9 |
| title | An introduction to applied multivariate analysis |
| title_auth | An introduction to applied multivariate analysis |
| title_exact_search | An introduction to applied multivariate analysis |
| title_exact_search_txtP | An introduction to applied multivariate analysis |
| title_full | An introduction to applied multivariate analysis Tenko Raykov ; George A. Marcoulides |
| title_fullStr | An introduction to applied multivariate analysis Tenko Raykov ; George A. Marcoulides |
| title_full_unstemmed | An introduction to applied multivariate analysis Tenko Raykov ; George A. Marcoulides |
| title_short | An introduction to applied multivariate analysis |
| title_sort | an introduction to applied multivariate analysis |
| topic | Multivariate analyse gtt Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd |
| topic_facet | Multivariate analyse Multivariate analysis Multivariate Analyse Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016593280&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT raykovtenko anintroductiontoappliedmultivariateanalysis AT marcoulidesgeorgea anintroductiontoappliedmultivariateanalysis |
Indexes
THWS Schweinfurt Zentralbibliothek Lesesaal
| Call Number: |
2000 QH 234 R266 |
|---|---|
| Copy 1 | ausleihbar Checked out – Due: 31.12.2099 Recall This |