Handbook of applied multivariate statistics and mathematical modeling:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
San Diego [u.a.]
Acad. Press
2000
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXVIII, 721 S. |
| ISBN: | 0126913609 |
Internformat
MARC
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| 245 | 1 | 0 | |a Handbook of applied multivariate statistics and mathematical modeling |c ed. by Howard E. A. Tinsley ... |
| 264 | 1 | |a San Diego [u.a.] |b Acad. Press |c 2000 | |
| 300 | |a XXVIII, 721 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Multivariate Analyse - Mathematisches Modell | |
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Datensatz im Suchindex
| _version_ | 1804128333280051200 |
|---|---|
| adam_text | CONTENTS
CONTRIBUTORS xxi
PREFACE xxv
I INTRODUCTION
I Multivariate Statistics and
Mathematical Modeling
HOWARD E. A. TINSLEY AND STEVEN D. BROWN
I. Data Preparation 8
A. Accuracy 8
B. Missing Data 10
C. Outliers 12
II. Study Your Data 14
VI CONTENTS
III. Selecting a Statistical Technique 15
IV. Data Requirements 17
A. Level of Measurement 17
B. Assumptions 17
V. Interpreting Results 22
A. Shrinkage Estimates 22
B. Cross Validation 23
C. Bootstrapping and Jackknifing 23
VI. Statistical versus Practical Significance 25
VII. Overview 27
A. Part 1: Introduction 27
B. Part 2: Multivariate Statistics 28 ,
C. Part 3: Mathematical Models 31
References 34
i
2 Role of Theory and Experimental Design in
Multivariate Analysis and Mathematical
Modeling ¦
JOHN HETHERINGTON
I. The Importance of Theory in Scientific Methodology 37
A. Strong Theory versus Law of the Instrument 40
B. Need for Theory in Multivariate Research 42
C. Design Implications for Multivariate Analysis 46
II. The Evolution of Postpositivist Scientific Method 48
A. Naive Inductivism 49 ,
B. Logical Positivism (Sophisticated Inductivism) 50
C. Popper s Falsificationism 51
D. Postpositivism (Modern Inductive Hypothetico
deductive Method) 53
III. Criticisms of Modern Inductive Hypothetico deductive ¦
Method 53
A. Historicism (Kuhn s Paradigms) 53
B. Anarchism (Feyerabend s Relativism) 55
C. Constructivism 56 i
IV. Critical Multiplism (Postpositivist Inductive Hypothetico
deductive Method) 57
V. Conclusion 59
References 60
i
CONTENTS Vil
3 Scale Construction and Psychometric
Considerations
RENE V. DAWIS
I. Introduction 65
II. Scale Definition 68
A. A Psychological View 68
B. Categories of Scales 69
III. Scale Construction 71
A. Scale Design 71
B. Item Construction 72
C. Item Selection 74
D. Scale Validation 78
E. Scale Evaluation 78
IV. Scaling Methods 79
A. Thurstone Scaling 79
B. Likert Scaling 80
C. Guttman Scaling 81
D. Paired Comparisons 82
E. Other Ranking Methods 83
F. Rating Methods 83
G. Empirical Scaling 84
H. Q Sort 85
V. Psychometric Considerations 86
A. The Attenuation Paradox 86
B. Reliability 86
C. Validity 87
D. Cross Validation 89
E. Bias and Equivalence between Groups 90
VI. A Final Word 92
References 92
4 Interrater Reliability and Agreement
HOWARD E. A. TINSLEY AND DAVID J. WEISS
I. Agreement versus Reliability 96
II. Level of Measurement 101
III. Type of Replication 102
IV. Interrater Reliability 103
A. Between Raters Variance 104
ViH CONTENTS
B. Reliability of Composite Ratings 107
C. Reliability When Variance Is Low 109
V. Interrater Agreement 111
A. Nominal Scales 112
B. Ordinal and Interval Scales 114
VI. Summary of Recommendations 117
References 118
5 Interpreting and Reporting Results
MARK HALLAHAN AND ROBERT ROSENTHAL
I. Introduction 125
II. Graphical Displays and Exploratory Data Analysis 126
A. Graphical Displays 126
B. Exploratory Data Analysis 129
III. Contrasts 132 j
A. Contrast Weights 132 i
B. Benefits of Contrasts 133
IV. Interpreting Significance Levels 133
A. Criticisms of Null Hypothesis Significance
Testing 133 !
B. Alternatives to Null Hypothesis Significance
Testing 136
V. Interpreting the Size of Effects 138
A. Problems 138
B. Solutions 138
C. How Large an Effect Is Important? 139
VI. Understanding Assumptions 140
A. Between Subjects Comparisons 140
B. Within Subjects Comparisons 142
VII. Process 143
A. Formulate Data Analysis Plan Prior to Data Col¬
lection 144
B. Use Statistical Consultants Appropriately 145
C. Use Statistical Software Appropriately 145
D. Focus on Scientific Understanding 146
VIII. Conclusion 146
References 147 ,
CONTENTS ix
II MULTIVARIATE ANALYSIS
6 Issues in the Use and Application of Multiple
Regression Analysis
ANRE VENTER AND SCOTT E. MAXWELL
I. Overview of Multiple Regression 152
A. The Prediction Explanation Dichotomy 152
B. Conclusion 156
II. Assumptions and Robustness 156
A. Accuracy of Description 157
B. Inferential Estimation and Testing 158
C. For Causal Inferences 159
III. Regression Diagnostics and Transformations 160
A. Introduction 160
B. Box Cox Transformation 161
C. Data Set and Regression Model Description 162
D. Diagnostics and Transformations 163
E. To Transform or Not to Transform? 168
F. Identifying Influential Observations 170
IV. Interactions and Moderator Effects 171
A. Rationale and Mechanics 172
B. Interpretation of the Interaction 173
C. Further Considerations 174
V. Sample Size Requirements for Multiple Regression
Analyses 175
A. Sample Size Requirements for Prediction 175
B. Sample Size Requirements for Explanation 176
VI. Handling Missing Data 177
A. Listwise Deletion 178
B. Pairwise Deletion 178
C. Traditional Imputation Methods 179
D. Possible Solutions 179
VII. Conclusion 180
References 181
7 Multivariate Analysis of Variance and Covariance
CARL J HUBERTY AND MARTHA D. PETOSKEY
I. Overview 183
A. Research Example 184
B. Computer Programs 184
X CONTENTS
II. Purpose of Multivariate Analysis of Variance 185
III. Design 185
A. Grouping Variable (s) 185 •
B. Response Variables 186
C. Sampling 187
D. Sample Size 188
IV. Analysis Guidelines 189
A. Data Characteristics 189
B. Analysis Sequence 191
C. Additional Analyses 199
D. Two Factor Multivariate Analysis of Variance 201
E. Multivariate Analysis of Covariance 202
V. Recommended Practices 204
A. Design 205
B. Analysis 205
C. Interpretation 206
D. Description 206
References 207
8 Discriminant Analysis
MICHAEL T. BROWN AND LORI R. WICKER
I. Introduction 209
II. Illustrative Example 210
III. Descriptive Discriminant Analysis 211
A. Data Requirements for Discriminant Analysis 211
B. Components of Discriminant Analysis Results 218
C. Interpreting Discriminant Functions 221
D. Rotating Discriminant Functions 222
E. Evaluating the Importance of Functions 222
F. Evaluating Classification Accuracy 225
IV. Predictive Discriminant Analysis 230
V. Other Issues and Concerns 232
A. Following up Multivariate Analysis of Variance 232 ,
B. Stepwise Discriminant Analysis 233
C. Reporting the Results of a Discriminant Analysis 233
VI. Conclusion 234
References 234
9 Canonical Correlation Analysis
ROBERT M. THORNDIKE
I. Appropriate Research Settings 237
A. An Example 238
CONTENTS Xi
II. General Taxonomy of Relationship Statistics 238
III. How Relations Are Expressed 241
A. Results from the Kleinknecht et al. (1997) Study 242
IV. Tests of Significance 243
V. Variance Accounted for—Redundancy 244
A. Vocabulary for Canonical Analysis 244
B. Computing Redundancy 248
C. Redundancy as the Average Squared Multiple
Correlation 250
VI. Interpreting the Components or Variates 251
A. Differences between Weights and Loadings for
Interpretation 251
B. Rotating Canonical Components 253
C. Rotated Components in the Kleinknecht et al. (1998)
Study 253
VII. Methodological Issues in Canonical Analysis 256
A. Stepwise Procedures 256
B. Estimating Bias in a Canonical Correlation 257
VIII. Concluding Remarks 260
References 261
10 Exploratory Factor Analysis
ROBERT CUDECK
I. Exploratory Factor Analysis 265
A. The Regression Connection 266
B. Factor Analysis and Partial Correlation 267
C. What Is a Factor Analysis? 268
D. The Factor Analysis Model 269
E. Example 271
F. The Rotation Problem 272
II. Factor Analysis and Principal Components 274
III. Estimating the Parameters 275
A. Method of Estimation 275
B. Number of Factors 277
C. Example 280
D. Analytic Rotation of Factors 282
E. Example 285
IV. Standard Errors for Parameter Estimates 286
V. Target Rotation 288
VI. Case Study 290
XH CONTENTS
VII. Summary 293
References 295
11 Cluster Analysis
PAUL A. GORE, JR.
I. General Overview 298
II. Uses for Cluster Analysis 300
III. Cluster Analysis Methods 301
A. Theory Formulation 301
B. Measures of Association 303
C. Clustering Algorithms 308
D. Hierarchical Methods 308
E. Partitioning Methods 313 ,
F. Overlapping and Ordination Methods 314
G. Empirical Investigations of Cluster Methods 314
H. Deciding on the Number of Clusters to Interpret 315
I. External Validity 316
J. Presenting Cluster Analysis Results 317 :
IV. Conclusion 318
References 318
12 Multidimensional Scaling
MARK L. DAVISON AND STEPHEN G. SIRECI
I. Proximity Data 325 :
II. Model and Analysis 326
A. Weighted Euclidean Model 328
B. Generalized Euclidean Model 329
III. Conducting a Multidimensional Scaling 329 ,
A. Selection of Stimuli and Participants 330
B. Selecting a Proximity Measure 330
C. Gathering Direct Proximity Data 331
D. Choosing an Appropriate Scaling Model: Weighted
versus Unweighted Models 334
E. Determining Dimensionality and Interpreting the
Solution 335
F. Interpreting Multidimensional Scaling Solutions 337
G. Rotation 339
H. Interpreting the Subject Space in Weighted Euclidean
Multidimensional Scaling 340
CONTENTS Xlii
/. Concluding Remarks in Selecting Dimensionality and
Interpreting the Solution 340
IV. Examples 341
A. Example 1: Direct Proximity Data 341
B. Example 2: Derived Proximity Data 343
C. Constrained Multidimensional Scaling 343
V. Multidimensional Scaling and Other Multivariate
Techniques 344
A. Cluster Analysis 344
B. Exploratory Factor Analysis 345
C. Item Response Theory 346
D. Circumplexes 347
VI. Concluding Remarks 347
A. Statistical Developments 347
B. Applications 348
References 349
13 Time Series Designs and Analyses
MELVIN M. MARK, CHARLES S. REICHARDT, AND LAWRENCE J. SANNA
I. Alternative Purposes of Time Series Studies 354
II. The Regression Approach to Fitting Trends 356
III. The Problem of Autocorrelation 359
IV. The Autoregressive Integrated Moving Average
Approach to Modeling Autocorrelation 360
A. Autoregressive Integrated Moving Average
Models 360
B. The Iterative Autoregressive Integrated Moving
Average Modeling Process 364
C. More on Transfer Function Modeling 373
D. Some Anticipated Advances 375
V. Multiple Cases 376
VI. Threats to Internal Validity in the Simple Interrupted
Time Series Design: Old and New Considerations 379
VII. More Elaborate Interrupted Time Series Designs 380
VIII. Elaboration in Time Series Studies of Covariation 381
IX. Design and Implementation Issues 382
A. Time Interval between Observations 383
B. Number of Time Points 383
C. Number of Cases 384
D. Archives as a Source of Data and Mediating
Processes 384
X. Summary and Conclusions 385
References 386
XIV CONTENTS
14 Poisson Regression, Logistic Regression, and
Loglinear Models for Random Counts
PETER B. IMREY
I. Preliminaries 391
A. Introduction 391
B. Scope of Application 392
C. Why Not Linear Models? 395
II. Measuring Association for Counts and Rates 397
A. Rate Ratios 397
B. Probability (Risk) Ratios 399
C. Odds Ratios 399
III. Generalized Linear Models 401
A. Exponential Family, Link Function, and Linear
Predictor 401 t
B. Likelihood Based Estimation and Testing 402
C. Hierarchical Models, Sufficient Statistics, and Marginal
Distributions 404
IV. Poisson Regression Models 405
A. Technical Overview 406 ¦
B. Respiratory Illness Rates among College Stu¬
dents 407
C. Firearm Suicide Rates 413
V. Logistic Regression Analysis 415
A. Technical Overview 416
B. Mammary Carcinogenesis in Rats 418
C. Variable Selection 420
D. Conditional Logistic Regression 423
VI. Loglinear Models for Nominal Variables 424
A. Technical Overview 425
B. Hierarchical Analysis of Variance Models for Three
Way Tables 427
C. Collapsibility and Association Graphs 429
D. Occupational Associations among Malaysian
Chinese 430
E. Logit Models as Loglinear Models 432
F. Simplified Structures for Ordinal Variables 433
VII. Exceptions 434
A. Overdispersion and Clustered Observations in
Generalized Linear Models 434
B. Population Averaged Models and Symmetry
Considerations 435
References 436
CONTENTS XV
III EVALUATION OF MATHEMATICAL MODELS
15 Structural Equation Modeling: Uses and Issues
LISABETH F. DILALLA
I. Defining Structural Equation Modeling 440
II. Common Uses of Structural Equation Modeling 441
A. Exploratory Factor Analyses 442
B. Confirmatory Factor Analyses 442
C. Regression Analyses 443
D. Moderator Mediator Analyses 444
III. Planning a Structural Equation Modeling Analysis 444
IV. Data Requirements 445
A. Multivariate Normality 445
B. Sample Size 447
V. Preparing Data for Analysis 447
A. Input Data Matrix 448
B. Missing Data 448
C. Construction of Input Matrix 449
D. Estimation Procedures 449
VI. Multiple Groups 450
VII. Assessing Model Fit 451
A. Absolute Fit Indices 451
B. Comparative Fit Indices 453
C. Summary 454
VIII. Checking the Output for Problems 454
A. Ensuring Accurate Input 454
B. Check for Warnings and Errors 456
IX. Interpreting Results 458
A. Examine Parameter Estimates 458
B. Examine Fit Indices 458
C. Examine Individual Aspects of the Model 460
D. Testing Nested Models 460
X. Conclusion 462
References 462
16 Confirmatory Factor Analysis
RICK H. HOYLE
I. Overview 466
A. Factors 466
XVi CONTENTS
B. Hypothesis Testing 468
C. Confirmatory versus Exploratory Factor
Analysis 469
II. Applications of Confirmatory Factor Analysis 469
A. Basic Questions about Dimensionality 469
B. Higher Order Models 470
C. Measurement Invariance 470
D. Construct Validation 470
E. Growth Models 471
III. Data Requirements 471
A. Sample Size 472
B. Distributional Properties 473
C. Scale of Measurement 473
D. Type of Indicator 474
TV. Elements of a Confirmatory Factor Analysis 474
A. Specification 474 (
B. A Word on Software 477
C. Estimation 477
D. Fit 482
E. Respecification 485
F. Parameter Estimates 487
V. Additional Considerations 489
A. Conceptual Inference 489
B. Statistical Inference 489
C. Statistical Power 490
VI. Conclusions and Recommendations 491
References 492
17 Multivariate Meta analysis
BETSY J. BECKER
I. What Is Meta analysis? 499
II. How Multivariate Data Arise in Meta analysis 501
A. Multiple Outcomes 501
B. Multiple Treatment Effects 502
III. Approaches to Multivariate Data 502
A. Treating Multivariate Data as Independent 503
B. Combining across Different Outcomes 504
C. Creating Independent Data Subsets 504
D. Modeling Dependence 504
CONTENTS XVH
IV. Specific Distributional Results for Common
Outcomes 506
A. Effect Sizes 506
B. Correlations 509
V. Approaches to Multivariate Analysis 512
A. Fixed Effects Models 512
B. Fixed Effects with Predictors 513
C. Random Effects Model 515
D. Mixed Model 515
E. Further Analyses for Correlations 516
VI. Examples of Analysis 516
A. Scholastic Aptitude Test Coaching 516
B. Postdivorce Adjustment of Children 519
VII. Summary 523
References 524
18 Generalizability Theory
GEORGE A. MARCOULIDES
I. Introduction 527
II. Fundamentals of Generalizabilitity Theory 529
A. A One Facet Crossed Design 530
B. Types of Error Variances 533
C. Generalizability Coefficients 534
D. Differences between Generalizability Studies and
Decision Studies 535
E. A One Facet Nested Design 536
III. Generalizability Theory Extended to Multifaceted
Designs 538
IV. Generalizability Theory Extended to Multivariate
Designs 542
V. Generalizability Theory as a Latent Trait Theory
Model 542
VI. Computer Programs 545
VII. Conclusion 546
References 546
19 Item Response Models for the Analysis of
Educational and Psychological Test Data
RONALD K. HAMBLETON, FREDERIC ROBIN, AND DEHUI XING
I. Introduction 553
II. Shortcomings of Classical Test Models 556
xviii contents
III. Introduction to Item Response Theory Models 557
A. Item Characteristic Functions or Curves 558
B. Item Response Theory Model Properties 559
C. Test Characteristic Function 561
D. Unidimensional Item Response Theory Models for
Fitting Polytomous Response Data 561
E. Multidimensional Item Response Theory Models 564
IV. Item Response Theory Parameter Estimation and Model
Fit 565
A. Assessing Item Response Theory Model Fit 568
V. Special Features of Item Response Theory Models 571
VI. Applications 573
A. Test Development 573
B. Computer Adaptive Testing 576
VII. Future Directions and Conclusions 578
References 579
20 Multitrait Multimethod Analysis
LEVENT DUMENCI
I. Random Analysis of Variance Model 586
II. Confirmatory Factor Analytic Model 593
III. Covariance Component Analysis 597
IV. Composite Direct Product Model 601
V. Conclusion 607
A. Choosing an Analytic Technique 608
References 609
21 Using Random Coefficient Linear Models for the
Analysis of Hierarchically Nested Data
ITA G. G. KREFT
I. Multilevel Models for Multilevel Data 613
II. Fields of Study Where Multilevel Data Analyses Can Be
Applied 614
A. Clinical Psychology 614
B. School Effectiveness Research 615
C. Family Research 616
D. Vocational Research 617
E. Summary 617
CONTENTS Xix
III. Random Coefficient Models Compared with Fixed
Linear Models 618
IV. Illustration of the Random Coefficient Model 619
A. Illustration and Model Specifications 621
B. Adding a School Context Variable to the Model 623
C. Explained Variance and Intraclass Correlation 625
V. Complex Random Coefficient Models 627
A. Models with Cross Level Interactions 627
B. Effect of Centering Explanatory Variables 631
C. Informed Use of Multilevel Models 633
D. Comparison of the Random Coefficient Model
versus Traditional Regression 635
VI. Summary 637
VII. Software 637
References 638
22 Analysis of Circumplex Models
TERENCE J. G. TRACEY
I. Exploratory Approaches to the Evaluation of
Circumplexes 644
A. Visual Inspection 644
B. Statistical Tests of the Circular Distribution 647
II. Confirmatory Approaches to the Evaluation of
Circumplexes 648
A. Constrained Multidimensional Scaling 649
B. Structural Equation Modeling 650
C. Randomization Tests of Hypothesized Order
Relations 655
III. Variations on Examining Circumplexes 658
A. Alternative Matrices 658
B. Correspondence Analysis 659
C. Loglinear Modeling 659
IV. Conclusions 659
References 660
23 Using Covariance Structure Analysis to Model
Change over Time
JOHN B. WILLETT AND MARGARET K. KEILEY
I. Latent Growth Modeling: The Basic Approach 666
A. Modeling Individual Change 666
XX CONTENTS
B. Mapping the Individual Growth Model onto the
LISREL Measurement Model 668
C. Modeling Interindividual Differences in Change 671
D. Mapping the Model for Interindividual Differences in
Change onto the LISREL Structural Model 672
II. Introducing a Time Invariant Predictor of Change into
the Analysis 677
III. Including a Time Varying Predictor of Change in the
Analyses 683
IV. Discussion 691
References 692
AUTHOR INDEX 695
SUBJECT INDEX 709
|
| any_adam_object | 1 |
| building | Verbundindex |
| bvnumber | BV013537434 |
| callnumber-first | Q - Science |
| callnumber-label | QA278 |
| callnumber-raw | QA278 |
| callnumber-search | QA278 |
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| id | DE-604.BV013537434 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:47:34Z |
| institution | BVB |
| isbn | 0126913609 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009242043 |
| oclc_num | 247391403 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-11 |
| owner_facet | DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-11 |
| physical | XXVIII, 721 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Acad. Press |
| record_format | marc |
| spelling | Handbook of applied multivariate statistics and mathematical modeling ed. by Howard E. A. Tinsley ... San Diego [u.a.] Acad. Press 2000 XXVIII, 721 S. txt rdacontent n rdamedia nc rdacarrier Multivariate Analyse - Mathematisches Modell Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Tinsley, Howard E. Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009242043&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Handbook of applied multivariate statistics and mathematical modeling Multivariate Analyse - Mathematisches Modell Mathematisches Modell (DE-588)4114528-8 gnd Multivariate Analyse (DE-588)4040708-1 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4040708-1 |
| title | Handbook of applied multivariate statistics and mathematical modeling |
| title_auth | Handbook of applied multivariate statistics and mathematical modeling |
| title_exact_search | Handbook of applied multivariate statistics and mathematical modeling |
| title_full | Handbook of applied multivariate statistics and mathematical modeling ed. by Howard E. A. Tinsley ... |
| title_fullStr | Handbook of applied multivariate statistics and mathematical modeling ed. by Howard E. A. Tinsley ... |
| title_full_unstemmed | Handbook of applied multivariate statistics and mathematical modeling ed. by Howard E. A. Tinsley ... |
| title_short | Handbook of applied multivariate statistics and mathematical modeling |
| title_sort | handbook of applied multivariate statistics and mathematical modeling |
| topic | Multivariate Analyse - Mathematisches Modell Mathematisches Modell (DE-588)4114528-8 gnd Multivariate Analyse (DE-588)4040708-1 gnd |
| topic_facet | Multivariate Analyse - Mathematisches Modell Mathematisches Modell Multivariate Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009242043&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT tinsleyhowarde handbookofappliedmultivariatestatisticsandmathematicalmodeling |