Identification, Equivalent Models, and Computer Algebra

1 Introduction 1.1 Themes of this Book 1.2 An Overview of the Book 1.3 Limitations 1.4 On Notation 1.5 Tie Commutation Matrix 1.6 Computer Algebra2 Identification, Equivalence and the Computerized Evaluation of Rank Conditions 2.1 Introduction 2.2 Basic Concepts 2.3 Identification and the Rank of the Information Matrix 2.4 The Jacobian Matrix Criterium 2.5 Prior Information 2.6 Handling the Rank in Practice 2.7 Partial Identification 2.8 Identification and Equivalence 2.9 The Exact Rank Analyzer (ERA)3 Simultaneous Equations Models 3.1 Introduction 3.2 The Conventional Simultaneous Equations Model 3.3 Simultaneous Equations Systems with Covariance Restrictions 3.4 An Example 3.5 A General Model 3.6 Simultaneous Equations Models with Measurement Error 3.7 An Example 3.8 Elaboration of the Example 3.9 Another Jacobian Matrix4 Identification in Factor Analysis Models 4.1 Introduction 4.2 The Jacobian Matrix in Confirmatory Factor Analysis 4.3 An Example 4.4 Exploratory Factor Analysis 4.5 The Indeterminacy Problem5 Restrictions on the Reduced Form and its Computerized Parametrization 5.1 Introduction 5.2 The Number of Restrictions on the Reduced Form 5.3 Exclusion Restrictions 5.4 Transformable Restrictions 5.5 A Minimal Parametrization 5.6 Examples of a Minimal Parametrization 5.7 An Algorithm for the Computation of a Minimal Parametrization of ¿ 5.8 MINPARAM 5.9 Examples of MINPARAM6 Identification in the Lisrel Model 6.1 Introduction 6.2 The Lisrel Model 6.3 Identification Using a Minimal Parametrization 6.4 Identification Using an Alternative Parametrization 6.5 An Example 6.6 Identification Using the Augmented Jacobian Matrix Method 6.7 Order Conditions for Lisrel Appendix: Derivation of the Jacobian Matrix for the Original Parameters7 Equivalence of Non-Nested Models 7.1 Introduction 7.2 Equivalence and Underidentification 7.3 Equivalence and Linear Manifolds 7.4 A General Condition for Equivalence 7.5 Equivalence of Systems of Simultaneous Equations8 Program Description 8.1 General Description 8.2 Main Programs 8.3 Subprograms 8.4 ERA 8.5 IDSIMCO and SIMCOJAC 8.6 IDSIMEV and SIMEVJAC 8.7 IDFAC and FACJAC 8.8 IDLISEX and LISEXJAC 8.9 IDLIS and LISJAC 8.10 MINPARAM 8.11 LISORDER 8.12 EQUISIMBibliographySubject IndexAuthor Index