GRA 5917: Input Politics and Public Opinion Logistic regression in political economy GRA 5917 Public Opinion and Input Politics. Lecture, September 9th 2010 Lars C. Monkerud, Department of Public Governance, BI Norwegian School of Management

First, though: Interaction effects in basic regression analysis (from last week)… Given the model… …simple rearrangment yields that is…

Interaction effects in basic regression analysis Model with interaction terms… …entails symmetry: Effect of one variable contingent on the other and vice versa …terms are mostly not to be interpreted in isolation:  A effect of X A when X B =0 (but, consider centering of variables to rescale an interesting value of X B to 0);  AB tells whether effect of X A (X B ) on Y depends on X B (X A ) for some values of X B (X A ) …additive terms are not to be seen as unconditional effects; little sense in asking of effect of X k in general

Interaction effects in basic regression analysis In model with interaction terms both the effect and… …the significance of the effect of one varaible varies with value of other variable: that is…

Interaction effects in basic regression analysis Need estimated variances and covariances. In SPSS: Click statistics Request variance- covariance matrix

Interaction effects in basic regression analysis Variance-covariance matrix:

Interaction effects… an example: Government duration govdur: Average duration of governments in parliamentary systems after WWII (in months), PS: Average parliamentary support as a percentage of seats held in the assembly, NP: Average number of parties in the government coalition, PD: A measure of party discipline… in the following model:

Interaction effects… an example: Government duration 1) in SPSS dataset gvmnt_duration.sav (downloaded from It’s Learning) create interaction variable NPPS (Transform > Compute Variable). Output descriptive statistics (max., min., mean) for the variables in the dataset 2) run a regression (Analyze > Regression > Linear) with the model and request Covariance matrix under Statistics

Interaction effects… an example: Government duration Estimates of  k Estimates of variances and covariances

Interaction effects… an example: Government duration 3) in a spreadsheet (Excel) use estimates (B) to map expected marginal effects of increasing the number of parties (NP) as it depends on reasonable (i.e. observed) values for parliamentary support (PS): and covariances and an appropriate t-value to find confidence intervals for the effect at different values of PS:

Excercise (I) 1)Download the social_welfare.sav file for It’s Learning (under today’s lecture). To see whether gender and partisanship are substitutes or (complements) when it comes to explaining factors influencing views on the social welfare-state you run the following regression: What is the difference in attitudes between females and males within the Democratic party? And within the Republican party? Are diffrences significantly greater in the one party as compared to the other? Use the results from the regression to map expected gender differences and their (95%) confidence intervals.

Excercise (II) 1)Under today’s lecture on It’s Learning download the lr_md2.sav data that combines the left-right self placement median etsimate from the 1990s with Persson and Tabellini’s economic and institutional data (the 85cross…sav). Construct interaction terms between the LR estimate (md_est) and the institutional indicators (propres2, majpar2 etc.) and perform a regression where you include these intarction terms. Analyze the effect of changing from a proportional parliamentary system to a majoritarian parliamentary system as the electorate’s ideological position changes (a la Gable and Hix (2005; figure2)). Compare the results to G&H’s original result.

Logistic regression Appropriate for categorical dependent variables, e.g. ”yes” vs. ”no” responses, voting for party X or not, acheiving an MSc degree or not, etc…. A popular model for the simple binary response (1=sucess vs. 0=failure) is the binary Logit model: … where P is the probability of y=1 (”success” or ”yes”, say)

Logistic regression Wheras L may vary between ∞ and - ∞, it is easily seen that P (reasonably) stays within the 0-1 range: i.e. the odds of ”success” vs. ”failure”; e  is the odds-ratio (OR)

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:

Logistic regression in SPSS Choose Analyze > Generalized Linear Models

Logistic regression in SPSS 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= ·X for X ranging from -4 to 10

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