Notes

Outline

Seven Steps to Build a GOOD Regression Model                        Dr. Alex Liu Southern California Political Methodology Program Feb 15, 2002 UC Riverside

The Background Some Pol Scientists easily abandon the simplicity of OLS and Linear Regression for not known the new and complicated technique (Beck 2000) Pol Scientists should use GOOD regression models Gap between Statistics, econometrics and political methodology The speaker happens to teach econometrics and political methodology to Ph.D. Candidates at USC N. Beck 2000 Political Methodology – A Welcoming Discipline

What is a GOOD Model ? Assumptions

Seven Steps to Build a GOOD Model Try to develop a simple procedure that allows us to build GOOD regression models easily and use simple software packages like SPSS Step 1: Graphically Explore & OLS to Estimate the Initial Model Step 2: Check ALL the Assumptions to Find Problems Step 3: Take Care of Outliers & Treat Collinearity and Dummy Variables Step 4: Use Variable Transformation to Correct ALL the Problems Detected Step 5: Select a best set of your variables Step 6: Final Diagnostics to Ensure your model is GOOD Enough Step 7: Estimate All the Coefficients & Present Your Results

Example: Political Confidence Dependent Variable: PolConf – General measure of political confidence on legal system, federal government, pol parties, parliament – 4 ~ 12 7 Independent Variables: Left ~ Right (1 left … 10 Right) Church (church attendance 1 more than once a week … 7 practically never) Age Education Income Postmaterialism/materialism (0 ~ 5 post) Marriage status (1 married, 2 living together, 3 divorced, 4 separated, 5 widowed, 6 single)

Step 1: First OLS Results Conduct Added Variable Plots to Help Specify Your Model Put all your variables in & Estimate all your coefficients by using OLS (Ordinary Least Square) Method

Example for Step 1

Step 2: Diagnostics 1 Check All the Assumptions: Var(ei)=ơ2 – Do Residuals Plots Cov(ei, ej)=0 – Calculate Durbin-Watson Value    (usually no auto correlation problem with pol data) ei ~ Normal Dist – Q-Q Plot Linearity – Plots (inverse variable plot)

Example for Step 2 Durbin-watson = 1.822

Step 3: Diagnostics 2 Collinearity and Outliers – Use VIF Values & Condition Index AND Studentized Residuals Using Dummy Variables

Example for Step 3 Identified about 6% Outliers by Using Studentized Residuals & Deleted them (study them separately is also recommended) No collinearity Problem as  VIF < 4   Condition Index < 18 Recode Married into a Dummy Variable 1 – married or    living together 0 - others

Step 4: Variable Transformation Correct ALL the Problems Detected in Step 2 Plus Non-linearity Use Power Function Family

Step 5: Model Assessment Select a best subset of variables Perform Partial F Test & Stepwise Methods

Example for Step 5  Use Backward Method Church, PostMaterialism, Edu, Medu, Mchurch, R2 = .168

Step 6: Diagnostics Again Step 2 Again If problem detected, repeat step 4

Example for Step 6 Durbin-watson = 1.938

Step 7: Final OLS Estimates If necessary, use other Non-OLS estimators