Handbook of Statistical Modeling for the Social and Behavioral Sciences

Transcription

1 Handbook of Statistical Modeling for the Social and Behavioral Sciences Edited by Gerhard Arminger Bergische Universität Wuppertal Wuppertal, Germany Clifford С. Clogg Late of Pennsylvania State University University Park, Pennsylvania and Michael E. Sobel University of Arizona Tucson, Arizona PLENUM PRESS NEW YORK AND LONDON

2 Contents Contributors Foreword by Donald В. Rubin Preface vii ix xii 1 Causal Inference in the Social and Behavioral Sciences 1 Michael E. Sobel 1 Introduction 1 2 Deterministic Causation in Philosophy 4 3 Probabilistic Causation: Variations on a Deterministic Regularity Account Philosophical Treatments Granger Causation in Economics 14 4 Causation and Statistics: An Experimental Approach 17 5 Causal Inference in "Causal Models" 27 6 Discussion 32 2 Missing Data 39 Roderick J. A. Little and Nathaniel Schenker 1 Introduction Examples Important Concepts Naive Approaches More Principled Approaches 46 2 Weighting Adjustments for Unit Nonresponse 46 3 Maximum Likelihood Assuming Ignorable Nonresponse Maximum-Likelihood Theory The Expectation-Maximization Algorithm Some Important Ignorable Maximum-Likelihood Methods Nonignorable Nonresponse Models Introduction Probit Selection Model Normal Pattern-Mixture Models 58 5 Multiple Imputation 59 xv

3 xvi Contents 5.1 Imputation Theoretical Motivation for Multiple Imputation Creating a Multiply Imputed Data Set Analyzing a Multiply Imputed Data Set 65 6 Other Bayesian Simulation Methods Data Augmentation The Gibbs Sampler The Use of Iterative Simulation to Create Multiple Imputations Discussion 69 3 Specification and Estimation of Mean Structures: Regression Models 77 Gerhard Arminger 1 Introduction 77 2 The Linear Regression Model Model Specification Estimation of Regression Coefficients Regression Diagnostics Multivariate Linear Regression 97 3 Maximum Likelihood Estimation Loglikelihood function Properties of the ML Estimator Likelihood Ratio, Wald, and Lagrange Multiplier Tests Restrictions on Parameters ML Estimation Under Misspecification Ill 5 Pseudo-ML Estimation Mean Structures The Linear Exponential Family Properties of PML Estimators Computation of PML Estimators With Fisher Scoring PML Wald and PML Lagrange Multiplier Tests Regression Diagnostics Under PML Estimation Quasi Generalized PML Estimation Specification of Mean and Variance Properties of PML Estimation With Nuisance Parameters Computation of QGPML Estimators QGPML Wald, Lagrange Multiplier, and Likelihood Ratio Tests Regression Diagnostics Under QGPML Estimation Univariate Nonlinear Regression Models Models for Count Data Standard Nonlinear Regression Models Models For Dichotomous Outcomes Quantit Models for Censored Outcomes Generalized Linear Models 153

4 Contents xvii 8 Multivariate Nonlinear Regression Models Models for Ordered Categorical Variables Models for Doubly Censored and Classified Metrie Outcomes Unordered Categorical Variables Generalized Estimating Equations for Mean Structures Software Specification and Estimation of Mean- and Covariance-Structure Models 185 Michael W. Browne and Gerhard Arminger 1 Introduction Background and Notation Scaling Considerations for Mean, Covariance, and Correlation Structures Fitting the Moment Structure Large Sample Properties of Estimators Lack of Fit of the Model and the Assumption of Population Drift Reference Functions and Correctly Specified Discrepancy Functions Computational Aspects Examples of Moment Structures The Factor Analysis Model Structural Equation Models Other Mean and Covariance Structures Mean and Covariance Structures with Nonmetric Dependent Variables Unconditional and Conditional Mean and Covariance Structures Inclusion of Threshold Models Conditional Polyserial and Polychoric Covariance and Correlation Coefficients Estimation Multigroup Analysis Example: Achievement in and Attitude toward High School Mathematics Software The Analysis of Contingency Tables 251 Michael E. Sobel 1 Introduction Introductory Examples Some Models for Univariate Distributions Measuring Association in the Two-by-Two Table: The Odds Ratio Odds Ratios for Two- and Three-Way Tables Odds Ratios for Two-Way Tables Odds Ratios for Three-Way Tables 265

5 XViÜ Contents 4 Models for the Two-Way Table Basic Models Models for Square Tables Models for Ordinal Variables Models for the Three-Way Table Basic Models Collapsibility in Models for the Three-Way Table Models for Tables with a One-to-One Correspondence among Categories Models for Tables With Ordered Variables Higher-Way Tables Estimation Theory Residual Analysis and Model-Selection Procedures Software GLIM BMDP SAS SPSS GAUSS CDAS S-Plus Latent Class Models 311 Clifford С Clogg^ 1 Introduction Computer Programs Latent Class Models and Latent Structure Models Basic Concepts and Notation The Model Defined and Alternative Forms MeasuringFit Alternative Forms of the Model An Example: Latent Classes in the American Occupational Structure Standard Latent Class Models for Two-Way Tables Some Related Models Research Contexts Giving Rise to Latent Classes and Latent Class Models Medical Diagnosis Measuring Model Fit with Latent Class Evaluation Models Rater Agreement Latent Class Models for Missing Categories Exploratory Latent Class Analysis and Clustering Predicting Membership in Latent Classes Latent Class Models in Multiple Groups: Categorical Covariates in Latent Class Analysis 340 t Deceased

6 XIX 11 Scaling, Measurement, and Scaling Models as Latent Class Models Ordinal X Classical Scaling Models The Rasch Model and Related Models Extending Latent Class Models to Other Scaling Contexts Conclusion 352 Panel Analysis for Metric Data 361 Cheng Hsiao 1 Introduction A General Framework The Basic Model A Bayes Solution Two Extreme Cases All Cross-Sectional Units Have the Same Behavioral Pattern versus Different Units Have Different Behavioral Patterns A Common Model for All Cross-Sectional Units Different Models for Different Cross-Sectional Units Variable Intercept Model Error Components Models Random Coefficients Models Mixed Fixed and Random Coefficients Models Random or Fixed Effects (Parameters) An Example Some Basic Considerations Correlations between Effects and Included Explanatory Variables Hypothesis Testing or Model Selection Conclusion 395 Panel Analysis for Qualitative Variables 401 Alfred Hamerle and Gerd Ronning 1 Introduction Some Regression Models for Binary Outcomes Probit Model, Logit Model, Linear Probability Model, and Maximum Likelihood Estimation Generalized Least Squares Estimation When There Are Repeated Observations A Note on Interpretation Models for Limited Dependent Variables Binary Regression Models for Panel Data The Fixed Effects Logit Model Random Effects Models Random Coefficients Models 422

7 XX Contents 3.4 Probit Models With Autocorrelated Errors Autoregressive Probit Models Panel Models for Ordinal Data Markov Chain Models Tobit Models for Panel Data Models for Count Data Poisson Distribution and Negative Binomial Distribution Mixtures of Poisson Distributions The Poisson Model A Model with Overdispersion Maximum Quasi-likelihood Estimation Under Overdispersion An Example with Cross-Sectional Data Panel Models for Count Data Analysis of Event Histories 453 Trond Petersen 1 Introduction Motivation The Hazard-Rate Framework Basic Concepts Discrete-Time Formulations Continuous-Time Formulations Time-Independent Covariates Time-Dependent Covariates Observability of the Dependent Variable Repeated Events Multistate Processes: Discrete State Space Multistate Processes: Continuous State Space Estimation Procedures Unobserved Heterogeneity Time-Aggregation Bias Continuous-Versus Discrete-Time Models Structural Models for Event Histories Sampling Plans A Conditional Likelihood for t a, given t b Likelihood for t b and Joint Likelihood for t a and t b Full Likelihood in t b, t a, and x Left Censoring Conclusion 512

8 Contents Xxi 10 Random Coefficient Models 519 Nicholas Т. Longford 1 Introduction An Illustration Clustered Design Models With a Single Explanatory Variable Patterns of Variation Contextual Models Terminology: A Review Applications The General Two-Level Model Categorical Variables and Variation Multivariate Regression as a Random Coefficient Model Contextual Models Random Polynomials Fixed and Random Parts Model Identification Estimation The Fisher Scoring Algorithm Diagnostics Model Selection Multiple Levels of Nesting Estimation Proportion of Variation Explained in Multilevel Models Generalized Linear Models Estimation Quasi-likelihood Extensions for Dependent Data Estimation for Models With Dependent Data Factor Analysis and Structural Equations Factor Analysis Structural Equation Models Example: Wage Inflation in Britain Software ML VARCL HLM Outlook 570 Index 579