Bekker / Merckens / Wansbeek Identification, Equivalent Models, and Computer Algebra

Statistical Modeling and Decision Science
1. Auflage 2014
ISBN: 978-1-4832-1639-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 224 Seiten, Web PDF

Identification, Equivalent Models, and Computer Algebra provides information pertinent to computer algebra. This book presents a brief discussion of the commutation matrix, an operator that plays a role when derivatives have to be evaluated involving symmetric matrices. Organized into eight chapters, this book begins with an overview of the link between identification of a parameter and the existence of a consistent estimator, and the link between identification of a model and the rank of a Jacobian matrix. This text then describes an algorithm for the determination of the exact rank of a parametrized matrix. Other chapters consider the identification in the simultaneous equation model. This book discusses as well the identification assessment in confirmatory factor analysis, a problem related to the simultaneous equations model. The final chapter deals with various computer programs that the enclosed diskette contains. This book is a valuable resource for readers who are interested in computer algebra.

Autoren/Hrsg.

Bekker, Paul A.

Merckens, Arjen

Wansbeek, Tom J.

Lieberman, Gerald J.

Olkin, Ingram

Inhaltsverzeichnis

1;Front Cover;1
2;Identification, Equivalent Models, and Computer Algebra;4
3;Copyright Page;5
4;Table of Contents;6
5;Acknowledgements;10
6;LIMITED WARRANTY AND DISCLAIMER OF LIABILITY;11
7;Chapter 1. Introduction;12
7.1;1.1 Themes of this book;12
7.2;1.2 An overview of the book;14
7.3;1.3 Limitations;16
7.4;1.4 On notation;17
7.5;1.5 Tie commutation matrix;18
7.6;1.6 Computer algebra;20
8;Chapter 2. Identification, equivalence and the computerized evaluation of rank conditions;26
8.1;2.1 Introduction;26
8.2;2.2 Basic concepts;27
8.3;2.3 Identification and the rank of the information matrix;30
8.4;2.4 The Jacobian matrix critérium;32
8.5;2.5 Prior information;35
8.6;2.6 Handling the rank in practice;39
8.7;2.7 Partial identification;42
8.8;2.8 Identification and equivalence;45
8.9;2.9 The Exact Rank Analyzer (ERA);50
9;Chapter 3. Simultaneous equations models;56
9.1;3.1 Introduction;56
9.2;3.2 The conventional simultaneous equations model;58
9.3;3.3 Simultaneous equations systems with covariance restrictions;61
9.4;3.4 An example;64
9.5;3.5 A general model;66
9.6;3.6 Simultaneous equations models with measurement error;68
9.7;3.7 An example;74
9.8;3.8 Elaboration of the example;78
9.9;3.9 Another Jacobian matrix;82
10;Chapter 4. Identification in factor analysis models;86
10.1;4.1 Introduction;86
10.2;4.2 The Jacobian matrix in confirmatory factor analysis;87
10.3;4.3 An example;91
10.4;4.4 Exploratory factor analysis;95
10.5;4.5 The indeterminacy problem;98
11;Chapter 5. Restrictions on the reduced form and its computerized parametrization;102
11.1;5.1 Introduction;102
11.2;5.2 The number of restrictions on the reduced form;103
11.3;5.3 Exclusion restrictions;105
11.4;5.4 Transformable restrictions;110
11.5;5.5 A minimal parametrization;113
11.6;5.6 Examples of a minimal parametrization;116
11.7;5.7 An algorithm for the computation of a minimal parametrization of II;119
11.8;5.8 MINPARAM;121
11.9;5.9 Examples of MINPARAM;125
12;Chapter 6. Identification in the Lisrel model;132
12.1;6.1 Introduction;132
12.2;6.2 The Lisrel model;135
12.3;6.3 Identification using a minimal parametrization;137
12.4;6.4 Identification using an alternative parametrization;138
12.5;6.5 An example;141
12.6;6.6 Identification using the augmented Jacobian matrix method;146
12.7;6.7 Order conditions for Lisrel;154
12.8;Appendix: Derivation of the Jacobian matrix for the original parameters;158
13;Chapter 7. Equivalence of non-nested models;168
13.1;7.1 Introduction;168
13.2;7.2 Equivalence and underidentification;170
13.3;7.3 Equivalence and linear manifolds;173
13.4;7.4 A general condition for equivalence;178
13.5;7.5 Equivalence of systems of simultaneous equations;182
14;Chapter 8. Program description;188
14.1;8.1 General description;188
14.2;8.2 Main programs;190
14.3;8.3 Subprograms;194
14.4;8.4 ERA;197
14.5;8.5 IDSIMCO and SIMCOJAC;198
14.6;8.6 IDSIMEV and SIMEVJAC;200
14.7;8.7 IDFAC and FACJAC;202
14.8;8.8 IDLISEX and LISEXJAC;203
14.9;8.9 IDLIS and LISJAC;205
14.10;8.10 MINPARAM;206
14.11;8.11 LISORDER;207
14.12;8.12 EQUISIM;208
15;Bibliography;210
16;Subject index;220
17;Author index;221