Linear causal modeling with structural equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, FL [u.a.]
CRC Press/Taylor & Francis
2009
|
| Schriftenreihe: | Statistics in the social and behavioral sciences series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 415 - 428 |
| Beschreibung: | XXIII, 444 S. graph. Darst. |
| ISBN: | 9781439800386 |
Internformat
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| 100 | 1 | |a Mulaik, Stanley A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Linear causal modeling with structural equations |c Stanley A. Mulaik |
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Datensatz im Suchindex
| _version_ | 1805084964283219968 |
|---|---|
| adam_text |
Titel: Linear causal modeling with structural equations
Autor: Mulaik, Stanley A.
Jahr: 2009
Contents
Preface. xiii
Acknowledgments. xxi
Author. xxiii
1 Introduction. 1
The Rise of Structural Equation Modeling. 1
An Example of Structural Equation Modeling. 4
Personality Descriptions as Variable Stimuli. 5
2 Mathematical Foundations for Structural Equation Modeling . 11
Introduction. 11
Scalar Algebra . 12
Vectors. 14
N-tuples as Vectors . 15
Equality of Vectors. 16
Scalars and Vectors . 17
Multiplying a Vector by a Scalar. 17
Addition of Vectors. 18
Scalar Product of Vectors. 18
Distance between Vectors. 19
Length of a Vector. 20
Another Definition for Scalar Multiplication. 21
Cosine of the Angle between Vectors. 21
Projection of a Vector onto Another Vector. 23
Types of Special Vectors. 24
Linear Combinations. 25
Linear Independence. 26
vi Contents
Basis Vectors. 26
Matrix Algebra. 26
Definition of a Matrix. 26
Matrix Operations. 27
Identity Matrix . 31
Scalar Matrix. 32
Diagonal Matrix. 32
Upper and Lower Triangular Matrices. 33
Null Matrix. 33
Transpose Matrix. 34
Symmetrie Matrices. 34
Matrix Inverse. 35
Orthogonal Matrices. 35
Trace of a Matrix. 36
Determinants. 37
Minors of a Matrix. 40
Rank of a Matrix. 40
Cofactors of a Matrix. 41
Expanding a Determinant by Cofactors. 41
Adjoint Matrix. 42
Important Properties of Determinants . 42
Simultaneous Linear Equations. 43
Treatment of Variables as Vectors . 44
Variables in Finite Populations. 45
Variables in Infinite Populations. 46
Random Vectors of Random Variables . 49
Maxima and Minima of Functions. 51
Slope as the Indicator of a Maximum or Minimum. 52
An Index for Slope. 53
Derivative of a Function. 54
Derivative of a Constant. 55
Derivative of Other Functions . 55
Partial Differentiation . 58
Maxima and Minima of Functions of Several Variables. 58
Constrained Maxima and Minima. 60
3 Causation. 63
Historical Background . 63
Causation among the Ancients. 65
Causation in the Seventeenth Century. 66
Descartes. 66
Locke. 67
Eighteenth-Century Empiricists. 69
Berkeley. 69
Hume . 69
Contents
Immanuel Kant. 70
Causation among Nineteenth-Century Empiricists. 75
Causation in the Twentieth Century. 75
Perception of Causation. 76
Hume's Doctrine. 76
Contemporary Cognitive Psychology. 77
J. J. Gibson. 77
Michotte. 77
Twardy and Bingham. 78
Wolff. 80
Lakoff and Johnson . 81
Causality. 82
Is Causality Material Implication? . 82
Is Causality a Functional Relation between Variables?. 83
Still, Why Variables? . 84
Causality and Counterfactuals. 85
Probabilistic Causality. 87
Local Independence. 91
Is Causation Manipulation?. 95
Conditions for Causal Inference. 100
Background Conditions. 100
Nonlinear Causation. 102
Science as Knowledge of Objects Demands Testing of Causal
Hypotheses. 104
Abduction, Deduction, and Induction. 104
Science is the Study of Objects. 106
Objects as Invariants in the Perceptual Field. 108
Implications for Structural Equation Modeling. 109
Summary and Conclusion. 110
4 Graph Theory for Causal Modeling. 111
Directed Acyclic Graphs. 111
Conditional Independence. 112
Markov Condition. 113
The Markov Condition. 114
d-Separation Criterion. 115
Minimality Condition . 116
Causal Minimality Condition. 116
Faithfulness Condition. 116
The Faithfulness Condition. 117
5 Structural Equation Models. 119
Basics of Structural Equation Models . 119
Path Diagrams. 120
From Path Diagrams to Structural Equations. 123
viii Contents
Formulas for Variances and Covariances in Structural Equation
Models. 125
Algebraic Methods. 125
Path Tracing Rules. 127
Matrix Equations. 134
6 Identification. 139
Incompletely Specified Models. 139
Freeing Parameters Implies No Added Constraints on
Their Value. 141
Identification. 142
Restricted versus Unrestricted Factor Analysis Models. 151
Identification of Metric. 152
7 Estimation of Parameters. 155
Discrepancy Functions. 155
Derivatives of Elements of Matrices . 157
Derivatives of Discrepancy Functions in Structural Equation
Modeling. 160
Estimation with Nonnormally Distributed Variables. 162
Asymptotic Distribution Free Estimation . 163
Maximum-Likelihood Estimation with Elliptical Distribution . . 166
Parameter Estimation Algorithms. 167
General Principles. 167
Method of Steepest Descent. 172
Cubic Approximation to Find Approximate Minimum. 174
The Newton-Raphson Algorithm. 179
Quasi-Newton Methods. 184
8 Designing SEM Studies. 187
Preliminary Considerations . 187
Multiple Indicators. 188
Multiple Indicators versus Single Indicators. 189
Tetrad Difference Tests with Multiple Indicators. 194
The Four-Step Procedure . 201
Some Problems That May Be Encountered with the Four-Step
Procedure. 208
Testing Invariance across Groups of Subjects. 210
Modeling Mean Structures. 214
Multigroup Comparisons of Mean Structures. 215
9 Confirmatory Factor Analysis . 219
Introduction. 219
Relation of Common Factor Model to Structural
Equation Model. 219
Contents
Early Attempts at Confirmatory Factor Analysis. 220
Multiple-Group Factor Analysis. 221
An Example of Confirmatory Factor Analysis. 221
Faceted Classification Designs. 227
Multirater-Multioccasion Studies. 228
Multitrait-Multimethod Covariance Matrices. 233
10 Equivalent Models. 241
Introduction. 241
Definition of Equivalent Models. 242
Replacement Rule. 242
Equivalent Models That Do Not Fit Every Covariance Matrix . 249
A Conjecture about Avoiding Equivalent Models by Specifying
Nonzero Parameters. 252
11 Instrumental Variables . 255
Introduction. 255
Instrumental Variables and Mediated Causation. 257
Conclusion. 260
12 Multilevel Models. 261
Introduction. 261
Multilevel Factor Analysis on Two Levels. 262
Multilevel Path Analysis. 265
13 Longitudinal Models. 269
Introduction. 269
Simplex Models. 269
Latent Curve Models. 277
Reality or Just Saving Appearances?. 281
14 Nonrecursive Models. 285
Introduction. 285
Flow Graph Analysis . 286
Open and Closed Paths. 288
Touching Paths . 289
Condensing Loops. 290
Mason's Direct Rule. 292
Covariances and Correlations with Nonrecursive Related
Variables. 297
Identification. 299
Estimation. ?1
Applications. 302
15 Model Evaluation . 307
Introduction. 307
Contents
Errors of Fit. 312
Chi-Square Test of Fit. 314
Satorra-Bentler Corrected Chi-Square Statistic. 317
Properties of Chi-Square and Noncentral Chi-Square. 317
Goodness-of-Fit Indices, CFI, and Others . 321
GFIs of LISREL. 321
CFI and Its Relatives. 325
Normed Fit Index. 325
CFI. 327
McDonald's µ* Index. 329
Tucker-Lewis (1973) Index. 330
The Meaning of Degrees of Freedom. 333
Generalization to Weighted Least-Squares Estimation. 337
Implications for Model Testing. 338
"Badness-of-Fit" Indices, RMSEA, and ER. 339
Exponentialized Negative RMSEA Index. 341
Parsimony. 342
Information Theoretic Measures of Model Discrepancy. 346
AIC Index. 346
AIC Index . 347
Variants of the AIC. 348
AIC Does Not Correct for Parsimony . 350
Kieseppä's Critique and a Rejoinder. 351
Is the Noncentral Chi-Square Distribution Appropriate?. 358
BIC. 360
Discussion. 361
Cross-Validation Index. 363
Confusion of "Likelihoods" in the AIC. 366
Other Information Theoretic Indices, ICOMP. 368
Complexity. 368
ICOMP. 371
LM, WALD, and LR Tests. 373
Expected Parameter Change. 380
Modifying Models Post Hoc. 381
Recent Developments. 382
Criticisms of Indices of Approximation. 387
Conclusion. 391
16 Polychoric Correlation and Polyserial Correlation. 395
Introduction. 395
Polychoric Correlation. 396
Overview . 398
Derivation. 399
Estimating All Parameters Simultaneously. 401
Contents
Two-Stage, Conditional Maximum-Likelihood Method. 403
Computing Estimates. 404
Polyserial Correlation. 408
Derivation. 409
Computation. 413
Evaluation. 414
References. 415
Index. 429 |
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| spelling | Mulaik, Stanley A. Verfasser aut Linear causal modeling with structural equations Stanley A. Mulaik Boca Raton, FL [u.a.] CRC Press/Taylor & Francis 2009 XXIII, 444 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics in the social and behavioral sciences series Literaturverz. S. 415 - 428 Social sciences / Mathematics Mathematik Sozialwissenschaften Social sciences Mathematics Graphentheorie (DE-588)4113782-6 gnd rswk-swf Kausalität (DE-588)4030102-3 gnd rswk-swf Strukturgleichungsmodell (DE-588)4252999-2 gnd rswk-swf Kausalität (DE-588)4030102-3 s Strukturgleichungsmodell (DE-588)4252999-2 s Graphentheorie (DE-588)4113782-6 s DE-604 DE-601 pdf/application http://www.gbv.de/dms/bowker/toc/9781439800386.pdf Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018944035&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mulaik, Stanley A. Linear causal modeling with structural equations Social sciences / Mathematics Mathematik Sozialwissenschaften Social sciences Mathematics Graphentheorie (DE-588)4113782-6 gnd Kausalität (DE-588)4030102-3 gnd Strukturgleichungsmodell (DE-588)4252999-2 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4030102-3 (DE-588)4252999-2 |
| title | Linear causal modeling with structural equations |
| title_auth | Linear causal modeling with structural equations |
| title_exact_search | Linear causal modeling with structural equations |
| title_full | Linear causal modeling with structural equations Stanley A. Mulaik |
| title_fullStr | Linear causal modeling with structural equations Stanley A. Mulaik |
| title_full_unstemmed | Linear causal modeling with structural equations Stanley A. Mulaik |
| title_short | Linear causal modeling with structural equations |
| title_sort | linear causal modeling with structural equations |
| topic | Social sciences / Mathematics Mathematik Sozialwissenschaften Social sciences Mathematics Graphentheorie (DE-588)4113782-6 gnd Kausalität (DE-588)4030102-3 gnd Strukturgleichungsmodell (DE-588)4252999-2 gnd |
| topic_facet | Social sciences / Mathematics Mathematik Sozialwissenschaften Social sciences Mathematics Graphentheorie Kausalität Strukturgleichungsmodell |
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