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GRA 5917: Input Politics and Public Opinion Basic regression (including interaction effects) in political economy Lars C. Monkerud, Department of Public Governance, BI Norwegian School of Management GRA 5917 Public Opinion and Input Politics. Lecture, September 2nd 2010 Excercise from last week… 3) The median measures in the WVS *AGGR.sav file are simply the response category code medians. For some variables (e.g. x011 - ”number of children”) this is an appropriate estimate of the substantive median. For other (continuous scale) phenomena a more reasonable median measure can be constructed. For instance, this is done in Gable and Hix (2005; see note 6) for the country-year median of the WVS e033 – ”left-right self positioning” variable. a) Using the methodology of Gable and Hix (2005), calculate the median for e033 for all combinations of countries and years in the WVS surveys. Save the estimates md_est in a file called lr_md.sav containing country-year observations for the median estimate and the identifiers (cname and year). (Tip: Work with a trivariate individual level file, count individuals in and out of the median category, aggregate and keep aggergates in the file until the final stage…) Regression analysis… • Given the correct model… y 0 A X A B X B e … and XA and XB are correlated… and e (as usual) a random individual error unrelated to any X… • excluding XB from etsimation will give biased estimate of XA… (unmeasured XB will be included in the error term) • but, if XA and XB are uncorrelated, omitting XA or XB will give correct effect estimates (betas)… Regression analysis in SPSS OLS regression with Analyze > Regression > Linear… Regression analysis in SPSS Move the dependent and independent variables to Dependent and Independent(s) frames respectively + a host of options (for selecting different models, assessing improved model fit, requesting covariances etc.) Excercises (I) 1) Like Gabel and Hix (2005), you would like to look into the relationship between a country’s electoral system and form of governement on the one hand and governement spending on the other, and how this might be viewed after one takes into account popular spending preferences. Download and save P&T’s 85cross…sav set from It’s Learning (the folder containing today’s lecture material) and… a) manipulate the lr_md.sav data that you have just assembled, keeping the earliest record from the 1990s with a valid md_est value. Are there any differences between records in this data and the data put to use by Gable and Hix (2005; Appendix)? b) Combine the manipulated lr_md.sav data with the data in the 85cross…sav and peform a regreession analyses where the spending varaiable cgexp is regressed on the variables in Gabel and Hix’s analyses named Original and model 1 (Gabel and Hix 2005; table 1). Next, do a regression where you also include md_est as a regressor. Compare the results to G&H’s result and P&T’s original result? Estimated marginal effect (): A large effect in substantive terms? Standard error: Measure of uncertainty of Corresponding t-test (t=/std.err.) for rejecting H0: =0 Interaction effects in basic regression analysis • Given the model… y 0 A X A B X B AB X A X B e …simple rearrangment yields y 0 ( A AB X B ) X A B X B e or y 0 ( B AB X A ) X B A X A e that is… y / X A A AB X B or y / X B B AB X A 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 XA when XB=0 (but, consider centering of variables to rescale an interesting value of XB to 0) …additive terms are not to be seen as unconditional effects Interaction effects in basic regression analysis • In model with interaction terms… …significance of effect of one varaible varies with value of other variable: var(y / X A ) var( A ) var( AB ) X B2 cov( A , AB ) 2 X B that is… se(y / X A ) var(y / X A ) , with CI y / X A t se(y / X A ) Interaction effects in basic regression analysis • Need estimated variances and covariances. In SPSS: Click statistics Request variancecovariance matrix Interaction effects in basic regression analysis • Variance-covariance matrix: XA XB XC XA XB XC var(X A ) cov(X B , X A ) cov(X C , X A ) cov(X A , X B ) var(X B ) cov(X C , X B ) cov(X A , X C ) cov(X B , X C ) var(X C )