Semiparametric Regression for the Social Sciences

Nonparametric smoothing techniques allow for the estimation of nonlinear relationships between continuous variables. In conjunction with standard statistical models, these smoothing techniques provide the means to test for, and estimate, nonlinear relationships in a wide variety of analyses. Until recently these methods have been little used within the social sciences. Semiparametric Regression for the Social Sciences sets out to address this situation by providing an accessible introduction to the subject, filled with examples drawn from the social and political sciences.

Readers are introduced to the principles of nonparametric smoothing and to a wide variety of smoothing methods. The author also explains how smoothing methods can be incorporated into parametric linear and generalized linear models. The use of smoothers with these standard statistical models allows the estimation of more flexible functional forms whilst retaining the interpretability of parametric models. The full potential of these techniques is highlighted via the use of detailed empirical examples drawn from the social and political sciences. Each chapter features exercises to aid in the understanding of the methods and applications.

Semiparametric Regression for the Social Sciences is supported by a supplementary website containing all the datasets used and computer code for implementing the methods in S–Plus and R. The book will prove essential reading for students and researchers using statistical models in areas such as sociology, economics, psychology, demography and marketing.

List of Tables.

List of Figures.

Preface.

1 Introduction: Global versus Local Statistics.

1.1 The Consequences of Ignoring Nonlinearity.

1.2 Power Transformations.

1.3 Nonparametric and Semiparametric Techniques.

1.4 Outline of the Text.

2 Smoothing and Local Regression.

2.1 Simple Smoothing.

2.1.1 Local Averaging.

2.1.2 Kernel Smoothing.

2.2 Local Polynomial Regression.

2.3 Nonparametric Modeling Choices.

2.3.1 The Span.

2.3.2 Polynomial Degree and Weight Function.

2.3.3 A Note on Interpretation.

2.4 Statistical Inference for Local Polynomial Regression.

2.5 Multiple Nonparametric Regression.

2.6 Conclusion.

2.7 Exercises.

3 Splines.

3.1 Simple Regression Splines.

3.1.1 Basis Functions.

3.2 Other Spline Models and Bases.

3.2.1 Quadratic and Cubic Spline Bases.

3.2.2 Natural Splines.

3.2.3 B–splines.

3.2.4 Knot Placement and Numbers.

3.2.5 Comparing Spline Models.

3.3 Splines and Overfitting.

3.3.1 Smoothing Splines.

3.3.2 Splines as Mixed Models.

3.3.3 Final Notes on Smoothing Splines.

3.3.4 Thin Plate Splines.

3.4 Inference for Splines.

3.5 Comparisons and Conclusions.

3.6 Exercises.

4 Automated Smoothing Techniques.

4.1 Span by Cross–Validation.

4.2 Splines and Automated Smoothing.

4.2.1 Estimating Smoothing Through the Likelihood.

4.2.2 Smoothing Splines and Cross–Validation.

4.3 Automated Smoothing in Practice.

4.4 Automated Smoothing Caveats.

4.5 Exercises.

5 Additive and Semiparametric Regression Models.

5.1 Additive Models.

5.2 Semiparametric Regression Models.

5.3 Estimation.

5.3.1 Backfitting.

5.4 Inference.

5.5 Examples.

5.5.1 Congressional Elections.

5.5.2 Feminist Attitudes.

5.6 Discussion.

5.7 Exercises.

6 Generalized Additive Models.

6.1 Generalized Linear Models.

6.2 Estimation of GAMS.

6.3 Statistical Inference.

6.4 Examples.

6.4.1 Logistic Regression: The Liberal Peace.

6.4.2 Ordered Logit: Domestic Violence.

6.4.3 Count Models: Supreme Court Overrides.

6.4.4 Survival Models: Race Riots.

6.5 Discussion.

6.6 Exercises.

7 Extensions of the Semiparametric Regression Model.

7.1 Mixed Models.

7.2 Bayesian Smoothing.

7.3 Propensity Score Matching.

7.4 Conclusion.

8 Bootstrapping.

8.1 Classical Inference.

8.2 Bootstrapping An Overview.

8.2.1 Bootstrapping.

8.2.2 An Example: Bootstrapping the Mean.

8.2.3 Bootstrapping Regression Models.

8.2.4 An Example: Presidential Elections.

8.3 Bootstrapping Nonparametric and Semiparametric Regression Models.

8.3.1 Bootstrapping Nonparametric Fits.

8.3.2 Bootstrapping Nonlinearity Tests.

8.4 Conclusion.

8.5 Exercises.

9 Epilogue.

Appendix: Software.

Bibliography.

Author Index.

Subject Index.

Luke J. Keele Department of Political Science, Ohio State University, US Since acquiring his PhD, Dr Keele has published work in a number of international journals, including papers on this specific topic. He has also taught the material for the proposed book at Ohio State University and presented it at international meetings.Dr Keele is a political scientist by trade but has considerable experience in applying statistical techniques to social science applications.

"The strength of Keele′s book is that it offers clear, straightforward explanations of the models, illustrated with social science (primarily political science) applications. Applied social science researchers should be able to incorporate these methods in their own research relatively easily after reading this book." ( The Political Methodologist, 2009)