3J Non-parametric and Semi-parametric Methods (including Bootstrap)
Luke Keele, Penn State University
5 - 16 August (two week course / 35 hrs)
Detailed Course Outline [PDF]
Course Content
Data from research in the social sciences often violates one, if not all of the assumptions underlying the use of traditional parametric statistics. Non-parametric statistics are another group of tests for statistical inference, which do not make strict assumptions about the population from which the data have been sampled, and may be used for studies with small sample sizes, nominal or ordinal level data, and non-normally distributed variables. To put it another way, non-parametric tests require few if any assumptions about the shapes of the underlying population distributions. For this reason, they are often used in place of parametric tests if one feels that the assumptions of the parametric test have been too grossly violated (e.g. if the distributions are too severely skewed). This module covers a variety of non-parametric techniques. The module covers among other topics: bootstrapping, robust statistics, rank-based tests, permutation tests, and non-parametric regression models. The second week of the module focuses on non-parametric regression models such as lowess and spline smoothers that allow analysts to estimate non-linear relationships between continuous variables. We will also learn how to add smoothers to standard regression models. These models allow analysts to estimate more flexible functional forms while retaining the interpretability of parametric models. Smoothers also allow analysts to test the validity of the model functional form. The module utilizes a number of examples from the political science, sociology, psychology, and economics. Most of the data sets are from published work, and students will see how the techniques in the class change published results. The class will emphasize on hands-on data analysis.
Course Objectives
- Understand and use the bootstrap.
- Use non-parametric tests and contrast these with standard parametric statistical tests.
- Use robust methods that are resistant to outliers.
- Understand and estimate non-parametric regression model.
- Estimate and interpret semi-parametric regression models.
This module is suitable for any researcher who has a basic understanding of standard regression models including logistic and poisson regression.
Course Prerequisites
Students should be familiar with linear regression models, logistic regression and count models such as poisson regression. Students should have some experience estimating these models as well as interpreting them.
Representative Background Reading
Students should be able to make sense of the methods used in the following two articles:
Howell, William G. and David E. Lewis. 2002. "Agencies by Presidential Design." Journal of Politics. 64:4, 1095-1114
King, Gary, Michael Tomz and Jason Wittenberg. 2000. "Making the Most of Statistical Analyses: Improving Interpretation and Presentation." American Journal of Political Science. 44:2, 347-361.
Required Reading
Semi-parametric Regression for the Social Science by Luke Keele 2008. Wiley and Sons.
Bootstrapping: A Non-parametric Approach to Statistical Inference by Christopher z. Mooney and Robert Duval. Sage.
Non-parametric Statistics: An Introduction by Jean D. Gibbons. Sage.
Modern Methods for Robust Regression by Robert Andersen. Sage.