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Statistical Methods for Social Scientists

Eric A. Hanushek, John E. Jackson
Published Date: 
New York: Academic Press
374 pages
The aspects of this text which we believe are novel, at least in degree, include: an effort to motivate different sections with practical examples and an empirical orientation; an effort to intersperse several easily motivated examples throughout the book and to maintain some continuity in these examples; and the extensive use of Monte Carlo simulations to demonstrate particular aspects of the problems and estimators being considered. In terms of material being presented, the unique aspects include the first chapter which attempts to address the use of empirical methods in the social sciences, the seventh chapter which considers models with discrete dependent variables and unobserved variables. Clearly these last two topics in particular are quite advanced--more advanced than material that is currently available on the subject. These last two topics are also currently experiencing rapid development and are not adequately described in most other texts.

1 Empirical Analyses in the Social Sciences
Social Science Theory and Statistical Models
Fitting Models to Data
The Development of Stochastic Model
The Analysis of Nonexperimental Data and the Selection of a Statistical Procedure
Simple Methods
Review Questions
2 Estimation with Simple Linear Models
The Basic Model                                                                                     
Least Squares Estimators               
Two Examples            
Appendix: Properties of Summations            
Appendix: Calculus and the Minimization of Functions               
Review Questions
3 Least Squares Estimators: Statistical Properties and Hypothesis Testing
Properties of Least Squares Estimators
Distribution of b-A Monte Carlo Experiment            
Statistical Inference                           
Hypothesis Tests for Schooling/Earnings Model             
Appendix: Estimation of Schooling/Earnings Model Using SPSS Computer Program Review Questions
4 Ordinary Least Squares in Practice
Interpretation of Regression Coefficients             
Model Specification                                   
Model Specification and Multicollinearity in Practice           
Functional Forms                                      
Dummy Explanatory Variables                           
Review Questions         
5 Multivariate Estimation in Matrix Form
The Least Squares Estimators                                   
Least Squares in Matrix Notation                               
Properties of Least Squares                                    
Distributional Aspects of the Error Term                                 
Statistical Inference              
Multivariate Education Example                                 
Appendix: Proof of Best                         
Appendix: Proof of Unbiasedness of the Estimator of Variance
Review Questions
6 Generalized Least Squares
Heteroskedasticity and Autocorrelation           
Formal Statement of the Problem                  
Generalized Least Squares                        
Generalized Least Squares and Examples of Heteroskedasticity and Autocorrelation             
Generalized Least Squares and Weighted Regression               
Monte Carlo Simulation of Generalized Least Squares
Generalized Least Squares in Practice                      
Visual Diagnostics                                         
Dynamic Models                                             
Appendix: Derivation of Generalized Least Squares Estimator                                     
Appendix: Unbiased Estimator of Variance
Review Questions 
7 Models with Discrete Dependent Variables
The Problem of Estimating Models with Discrete Dependent Variables                              
Alternative Models-Dichotomous Dependent Variables              
Logit Analysis grouped Data                                
Logit Analysis-Microdata                                   
Probit Analysis                                            
An Example                                                 
Monte Carlo Simulation of Dichotomous Dependent Variables            
Polytomous Variables/Joint Distributions                   
8 Introduction to Multiequation Models
Two Examples of Structural Systems
Path Analysis
The General Multiequation Model
Estimating Hierarchical Models
Hierarchical, Nonrecursive Systems
Underidentification in Hierarchical Models
Nonrecursive Hierarchical Models: Two Examples
Appendix: Instrumental Variables Estimator
Review Questions
9 Structural Equations: Simultaneous Models
Identification in Simultaneous Systems: An Example                
Identification in Simultaneous Models            
Estimating Identified Models                     
Simultaneous Equations: The Voting and Aspiration Examples           
Identification through Assumptions about Error Terms            
Alternative Estimators            
Summary and Conclusions           
Appendix: Variances and Covariances for Peer Influence Data                      
Review Questions
10 Estimating Models with Erroneous and Unobserved Variables
Erroneous Explanatory Variables
Unobserved Variables
Factor Analysis
Linear Structural Models and the General Analysis of Covariances
Appendix I Statistical Review
Theoretical Distributions
Properties of Estimators
Hypothesis Testing
Maximum Likelihood (ML) Estimation
Appendix II Matrix Algebra
  Basic Properties
Basic Operations
Matrix Multiplication
Other Operations
Systems of Linear Equations
Existence of an Inverse-Rank
Review Questions for Appendix 11
Appendix III Statistical Tables References