1. GRA 5917 Public Opinion and Input Politics. Lecture September 16h 2010 Lars C. Monkerud, Department of Public Governance, BI Norwegian School of Management GRA 5917: Input Politics and Public Opinion Panel data regression in political economy

2. First, though: A short note on logistic regression (from last week)… L (the log-odds, the logit) theoretically varies between and -, but P (reasonably) stays within the 0-1 range: i.e. the odds of success vs. failure; e is the odds-ratio (OR)

3. Logistic regression Intuitively appealing since P=f(X k ) increases in L as factor X k changes, but slowly initially and as P approaches 1:

4. Logistic regression Extensions and special variants of the logit model: the multinomial logit model, which models responses in i=1 to n categories (with i=n the reference category) the ordinal logit model, which models responses in i=1 to n ordered categories (with i=n the reference category), assuming that the odds- ratio effect on the odds of a lower ordered event (i.e. numerator events vs. denominator events) is independent of the observed category response (aka the proportional odds model)

5. Logistic regression in SPSS Choose Analyze > Generalized Linear Models

6. Logistic regression in SPSS Choose Binary logistic A flexible tool with many possible model specifications

7. Logistic regression in SPSS Choose dependent variable Choose reference category, i.e. to model P(not in ref. category)

8. Logistic regression in SPSS Choose predictors: class variables (factors) or contiuous variables (covariates)

9. Logistic regression in SPSS Build model

10. Presenting changes in P(y=1) from logistic regression results Have estimated L=0.4+1.2·X for X ranging from -4 to 10

11. Presenting changes in P(y=1) from logistic regression results Have estimated L=0.4+1.2·X for X ranging from -4 to 10

12. Excercises (I) a)You are interested in how peoples age influences their general feeling of happiness. Use the XWVSEVS_1981_2000_v20060423.sav data set supplied under the PolEc Dataset folder on Its Learning. a)Create a new variable happy that takes on the value 1 if the individual in question reports to be happy (very or quite) and 0 otherwise. Run a simple binary logistic regression with happy as dependent variable and (continous) age (x003) and the indivuals houshold income (x047) as independent variables. Comment on the results and graph the realtionship between the probability of being happy and age (Tip: Use descriptive analysis to find the minimum and maximum of age, i.e. the range for which reasonable predictions of happiness can be made, and graph the relationship holding income level constant at the mean). b)Redo the analysis with year of birth (x003) added to the model. Comment on the results in the SPSS output and again graph the relationship between age and the probability of being happy (holding both year of birth and income cosntant at their respective means).

13. Analysis of panel data Given the correct model… A time-invariant covariate… …estimating the model will give unbiased estimates of A : the D k exhaust varaiation between cross–section units (i); i.e. influence from all observable and unobservable time-invariant variables are accounted for

14. Analysis of panel data in SPSS (I) OLS regression with country specific (and time specific) dummy variables added to the equation (as independent variables) with Analyze > Regression > Linear… problem: How create a large set of dummy variables? DO REPEAT d=c1 to c60 /i=1 to 60. * here, d defines the array of dummy variables that will be generated (c1, c2 to c60); The i controls the number of repeats. COMPUTE d=(cc=i). * computes the ith element in d (conveniently named ci) as 1 if cc=i, as 0 otherwise. END REPEAT. EXECUTE. Auto-recode the variable indexing the groups (e.g. individuals, countries by proper names) into a running numeric code (Transform > Automatic Recode…) 1) Recode group variable2) Create dummies with syntax, e.g.:

15. Analysis of panel data in SPSS (II) Or use the mixed models feature: Analyze > Mixed Models > Linear… (Maximum Likelihood estimation); creates group dummies from class variables automatically

16. Analysis of panel data in SPSS (II) Click Continue

17. Analysis of panel data in SPSS (II) Move the dependent variable into Dependent frame and class independents into Factor(s) and continuous independents into Covariate(s); choose REML estimation under Estimation… and Parameter Estimates under Statistics…

18. Analysis of panel data in SPSS (II) Click Fixed…

19. Analysis of panel data in SPSS (II) Mark variables that will appear in the Factors and Covariates frame and Add them to the Model frame. Click Continue

20. Analysis of panel data in SPSS (II) Click OK to start analysis

21. A note on within R 2 In the output from the mixed… procedure we get estimates of residuals: The often reported measure of within R 2 is simply: (Residual Model with group effects only – Residual Full Model ) / Residual Model with group effects only i.e. the proprortion of explainable variance (after group effects have been taken into account) that is explained by variables varying within groups

22. Analysis of panel data (II)… Instead of the model… …one could estimate the random effects model Valid if the group effect v i (viewed as a disturbance term) is uncorrelated with other regressors… (and RE estimator of A will be more efficient than the FE estimator)

23. Analysis of panel data in SPSS (II) Click Random and build random terms in same way as you would build fixed terms

24. Excercises (II) a)Use the 60panel…sav set supplied under todays lecture. a)Redo the P&Ts analysis in model (1) in table 3.2 (Persson and Tabellini 2005:44). Compare the results with those presented in the book. b)Redo the P&Ts analysis in model (2) and (3) in table 3.2 (Persson and Tabellini 2005:44). (Tip: Before analysis, use select cases using the criteria discussed on pp. 76-77 in P&T).