Sociology 602 Martin Lecture 15: May 14, 2002

1. Sociology 602 (Martin)Lecture 15: May 14, 2002 Details about next week�s final exam. Review for next week�s final exam. conceptual skills math skills examples for practice Final course evaluation

2. Details about the final Time and date: Tuesday, May 21, 6:30 � 8:30 p.m. Location: 2309 Art-Sociology (here) Materials: pens or pencils, calculators, two 4X6 note cards. I will provide: blue books, tables of p-values

3. Review for the final: Skills you needfrom the 1st half of the course. How to specify a regression model. How to interpret coefficients (and standard errors) in a regression model. How to find problems in a regression model. How to fix problems in a regression model.

4. Review for the final: Topicsfrom the 2nd half of the course. Comparing predictor variables and selecting models. NKNW 6.5, 7.1, 7.2, 7.3, 7.6 Model building, polynomials and interactions. NKNW 7.7, 7.8, 8.1, 8.3, 8.4 Diagnostics and remedial measures NKNW 9.1, 9.2, 9.4, 9.5, 10.1, 10.2, 10.6 Logistic regression NKNW 14.1, 14.2, 14.3, 14.4. Maximum likelihood and model building. NKNW 1.8, 14.3, 14.5, A.8 Experimental design and analysis of variance NKNW 16.116.1, 16.2, 16.6, 16.8, 16.11

5. Week 9: Comparing predictor variables and selecting models. Conceptual skills: be able to answer questions such as� A: what makes a variable important in a model? large b? small p-value? substantive importance? explained error? B: what are the uses of the various forms of R2? simple or multiple regression, adjusted or not. C: what is an extra sum of squares? D: What does �nested� mean? E: how can multicollinearity affect a regression model?

6. Week 9: Comparing predictor variables and selecting models. Math skills: be able to perform these tasks: A: compare SSE, SSR, and SSTO in nested models. B: use proper notation and calculate Extra Sums of Squares. C: decompose R2 in a multiple regression model D: do an F-test for extra sums of squares. E: look up and interpret p-values from an F-test.

7. Week 9: Comparing predictor variables and selecting models. practice example: Suppose you are given SAS outputs from two regression models: sums of squares, degrees of freedom, correlation coefficients for explanatory variables. (e.g. models X1 and X1,X2, page 2-3 of SAS readout for week 9) A: Use a hypothesis testing format to choose a preferred model. assumptions, null hypothesis, test statistic, p-value, conclusion. B: Discuss how multicollinearity might affect your choice of models, and your interpretation of the findings.

8. Week 10: Model building with variables, polynomials, and interactions conceptual skills: Be able to answer questions such as� A: When it is appropriate and helpful to add polynomial and interaction terms? B: Based on your priorities, which criteria should you choose for including variables in models? C: When you do a stepwise regression, why start with the variable that explains the most error?

9. Week 10: Model building with variables, polynomials, and interactions math skills: Be able to do the following. A: Find/sketch/interpret predicted values from polynomial models. B: Find/sketch/interpret predicted values from interaction models. C: Compare and interpret r2 , r2a, and Cp in an all-possible regressions procedure. D: Follow and interpret the readout from a SAS forward stepwise regression.

10. Week 10: Model building with variables, polynomials, and interactions practice example: Suppose you are given readouts related to two nested regression models: (e.g. step 2 vs step3, page 5 of SAS readout for week 10) A: use appropriate terminology to describe how the models are nested. B: Compare statistics on the two models. C: Choose the model you prefer, and defend your choice on appropriate grounds.

11. Week 11: Multiple regression diagnostics and remedial measures. conceptual skills: Be able to answer questions such as� A: What is the point of doing diagnostic and remedial measures? B: How is nonlinearity different in multiple regression than in simple regression? C: What are the logical weaknesses of tests such as the SPEC test, where h0 is that there is constant error variance. D: What are the techniques for model validation and why do we need them?

12. Week 11: Multiple regression diagnostics and remedial measures. math skills: Be able to do the following: A: Interpret a partial regression plot, and suggest remedies. B: Interpret a spec test, and suggest remedies. C: Interpret tests for influential observations, and suggest remedies. D: Interpret tests for multicollinearity, and suggest remedies.

13. Week 11: Multiple regression diagnostics and remedial measures. practical example: (example: notes from Week 11, pages 15-21) A: Given a set of SAS statistics on influence scores for individual observations, discuss what is happening and how to fix it. B: Given SAS output on a spec test, interpret results and suggest improvements in the model (if any). C: Given SAS output on VIF, interpret results and suggest improvements in the model (if any). D: Interpret SAS output for partial regression plots.

14. Week 12: Logistic regression conceptual skills: Be able to answer questions such as� A: Why don�t we normally use OLS regression in models with a binary outcome variable? B: What does an �odds� mean, conceptually and mathematically? C: In a model where log(p/(1-p)) = b0 + b1X, what does b1 tell us about the relationship between X and p? 

15. Week 12: Logistic regression math skills: Be able to do the following: A: calculate a probability, given a log odds. B: calculate a log odds, given a probability. C: calculate a probability, given X-values and coefficients in a regression equation. D: use probabilities to demonstrate the meaning of a b1 coefficient. E: use probabilities to demonstrate the meaning of a b0 coefficient.

16. Week 12: Logistic regression example: For a sample from some nation, a logistic regression model predicts whether a 1st time mother received prenatal care, based on whether the mother is a Muslim or some other religion (X1, Muslim = 1) and the years of education for the mother (X2) log (p/(1-p)) = -0.6 + 1.1X1 + 0.2X2 A: Find the predicted probability of receiving prenatal care for a non-Muslim with 6 years of education. B: What does �0.2� mean in this model? C: Use a pair of predicted proportions to help the reader understand the �effect� of an additional year of education.

17. Week 13: Model building with maximum likelihood models conceptual skills: Be able to answer questions such as� A: How is maximum likelihood estimation similar to or different from least squares estimation? B: When is maximum likelihood estimation necessary? C: What does it mean when one model has a higher likelihood than another?

18. Week 13: Model building with maximum likelihood models math skills: Be able to do the following: A: read SAS output produced by a maximum likelihood procedure such as a logistic regression. B: calculate a difference in �2 log likelihood, given two nested models. C: Do a likelihood ratio test, then interpret it.

19. Week 13: Model building with maximum likelihood models example: Given a SAS readout such as that on page one of the SAS log for week 13, explain� -2 log L for intercept only -2 log L for intercept and covariates parameter estimates for coefficients standard error estimates for coefficients �Wald Chi-square� statistics and p-values. For the same example, do a likelihood ratio test, select and justify a preferred model.

20. Week 14: Experimental design and Analysis of Variance conceptual skills: Be able to answer questions such as� A: Given a set of variables and a research question, which model is most appropriate (OLS, logistic, ANOVA) and why? B: What are the relative advantages and disadvantages of using ANOVA instead of regression in a case where you could use either one? C: (Know special ANOVA terms) D: (Compare statistical control with experimental control) E: (Compare randomization with random sampling)

21. Week 14: Experimental design and Analysis of Variance math skills: Be able to do the following: A: Sketch distributions of variables in �regression� style and in �ANOVA� style. B: Write a formal hypothesis test using readout from an ANOVA procedure. assumptions, hypothesis, test statistic, p-value, conclusion C: Identify and explain possible violations of ANOVA assumptions.

22. Week 14: Experimental design and Analysis of Variance example: Here are fictitious ANOVA results for a one-way anova (sexual harassment program example): Outcome: 3 yes/no (1/0) questions to assess whether respondent sees a situation as sexually coercive: High scores indicate high perceptions of sexual coercion. Experimental factor: whether a respondent was assigned (at random) to a sexual harassment training program or not.

23. Week 14: Experimental design and Analysis of Variance example (continued): Results: mean for men with training = 2.90 mean for men with no training = 2.78. F* = 5.49 (1,330) (Another possibility: I give you a SS table and you calculate F*) A: Conduct a formal hypothesis test, stating assumptions and hypotheses, listing test statistics, finding a p-value, and discussing a conclusion. B: Discuss how you might set up a similar study, bearing in mind issues of random sampling, randomization, and keeping costs down.

24. Course evaluation Things you did that worked well: homeworks in-class discussions Things that did not work well: promptness some e-mail interactions Things you should try: Develop a shared responsibility for statistical advice (for thesis and dissertation work)