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GRA 5917: Input Politics and Public Opinion Panel data regression in political economy Lars C. Monkerud, Department of Public Governance, BI Norwegian School of Management GRA 5917 Public Opinion and Input Politics. Lecture September 16h 2010 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: e e L P log 1 P P 1 P eL P 1 eL i.e. the odds of ”success” vs. ”failure”; eb is the odds-ratio (OR) Logistic regression • Intuitively appealing since P=f(Xk) increases in L as factor Xk changes, but slowly initially and as P approaches 1: 1 0.9 0.8 0.7 0.6 P 0.5 0.4 0.3 0.2 0.1 0 L(X) Logistic regression • Extensions and special variants of the logit model: Pi n b 0i b ki X k Logit i Li log Pi n cn Pi Logit c L c log i c1n b 0c b k X k 1 Pi i 1 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 oddsratio 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) Logistic regression in SPSS Choose Analyze > Generalized Linear Models Logistic regression in SPSS A flexible tool with many possible model specifications Choose Binary logistic Logistic regression in SPSS Choose dependent variable Choose reference category, i.e. to model P(not in ref. category) Logistic regression in SPSS Choose predictors: class variables (factors) or contiuous variables (covariates) Logistic regression in SPSS Build model 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 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 Excercises (I) a) You are interested in how people’s age influences their general feeling of happiness. Use the XWVSEVS_1981_2000_v20060423.sav data set supplied under the PolEc Dataset folder on It’s 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 indivual’s 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). Analysis of panel data A time-invariant covariate… • Given the correct model… yit b 0 b A X Ait b B X Bi eit …estimating the model N 1 yit b 0 b A X Ait D eit k k 1 k i will give unbiased estimates of bA: the Dk exhaust varaiation between cross–section units (i); i.e. influence from all observable and unobservable time-invariant variables are accounted for 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? 1) Recode group variable 2) Create dummies with syntax, e.g.: Auto-recode the variable indexing the groups (e.g. individuals, countries by proper names) into a running numeric code (Transform > Automatic Recode…) 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. 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 Analysis of panel data in SPSS (II) Click Continue 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… Analysis of panel data in SPSS (II) Click Fixed… 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 Analysis of panel data in SPSS (II) Click OK to start analysis A note on within R2 In the output from the mixed… procedure we get estimates of residuals: The often reported measure of within R2 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 Analysis of panel data (II)… • Instead of the model… N 1 yit b 0 b A X Ait D eit k k 1 k i …one could estimate the random effects model yit b 0 b A X Ait b B X Bi vi eit Valid if the group effect vi (viewed as a disturbance term) is uncorrelated with other regressors… (and RE estimator of bA will be more efficient than the FE estimator) Analysis of panel data in SPSS (II) Click Random and build random terms in same way as you would build fixed terms Excercises (II) a) Use the 60panel…sav set supplied under today’s lecture. a) Redo the P&T’s 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&T’s 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).