Interpre'ng our Results & Condi'onal Effects. Andrea Ruggeri WK 2 Q Step, Year 2

Transcription

1 Interpre'ng our Results & Condi'onal Effects Andrea Ruggeri WK 2 Q Step, Year 2

2 New Material Prepara:on Worksheet R on the Q- Step WebLearn

3 Goals of Lecture Interpreta:on of coefficients and their substan:ve interpreta:on Expected Y based on es:mates and quan::es of interests Graphical representa:on of regression Graphical representa:on of variables effects Interpre:ng Interac:ons

4 Roadmap Thinking about our results Tables Substan:ve effects Visualizing the effects Expected Y in different scenarios Condi:onal Effects / Interac:ons

5 Your Results When repor'ng your results in your essays, (most of ) you followed Lijhpart s tables style à highlight limita:ons When discussing your results (most of) you limited the discussion on effect direc'on and sta's'cal significance à substan:ve effect?

6 Lijphart table

7 How a table should look like? What we should show in a table? Different models in same table, why? Easier to compare/see different specifica:ons How Xs effects change adding controls Sample Size (N) Informa:on on Analy:cal Units (countries, years, dyads ) Quality of fit/ Model performance: for OLS R2.

8 Oil, Islam, and Women Ross, Michael L. "Oil, Islam, and women." American Poli-cal Science Review (2008):

9 What does explain democracy?

10 Dem=β0+β1 GDPpc+β2 Urban Popula:on

11 Dem=β0+β1 GDPpc+β2 Urban Popula:on Exp. Dem - 1,7 = - 3,484 (constant) +0,056 * 29,9 (=Median) +0,283*0.132(= Median) Exp. Dem 7,9 = - 3,484 (constant) +0,056 * 188,159 (=top5%) +0,283*3.3(= top 5%)

12 Exp. Dem = - 2,533 (constant) +0,020 * 188,159 (=top5%) +0,154*3.3(= top 5%) +8,364*0 (No Western) - 3,346*1(MENA) Exp. Dem 10 = - 2,533 (constant) +0,020 * 188,159 (=top5%) +0,154*3.3(= top 5%) +8,364*1 ( Western) - 3,346*0( No MENA) You could use real case (e.g. Senegal in 2000). Then change level of Xs and see varia:on of Y.

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16 Ross, Michael L. "Oil, Islam, and women." American Poli-cal Science Review (2008):

17 Gartzke, E. (2007). The capitalist peace. American Journal of Poli-cal Science 51(1),

18 I used the coefficients of Model 6. I hold all variables at their means and mul:ple by their coefficients; I calculate expected Democracy at different levels of GDP pc from 0$ to 43,000 $

19 Here I also calculated the confidence intervals

20 Evans, G., & Tilley, J. (2012). The depoli:ciza:on of inequality and redistribu:on: Explaining the decline of class vo:ng. The Journal of Poli-cs, 74 (04),

21 Hultman, Lisa, Jacob Kathman, and Megan Shannon. "United Na:ons peacekeeping and civilian protec:on in civil war." American Journal of Poli-cal Science 57.4 (2013):

22 Condi'onal Effects It depends or Mul'plica've Interac'on Models

23 Condi:onal Effects We discussed how you could calculate expected value of your Y, given certain levels of your Xs and your findings (βs). Different scenarios and graphs. But what if you want to know whether the effect of an X on Y is condi:onal to another dependent variable Z? Effect of X On Y Depending on Z GDP Democracy Natural Resources Educa:on Vo:ng Age Trade War Democracy

24 Interac:ons Regression Models so far: Dem=β0+β1 GDPpc+β2 Post Cold War What if we expect the effect of GDPpc on Democracy being different during two different historical periods? Cons:tu:ve Terms Dem=β0+β1GDPpc+β2 Post Cold War+ β3gdp*postcw Interac:on

25 Brambor, Thomas, William Roberts Clark, and Mav Golder Understanding Interac:on Models: Improving Empirical Analyses. Poli-cal Analysis 14 (1):

26 Aid, Peace, and Development Peace Development War Level of Aid

27 Y=β0+β1X+β2 Z+ β3xz à eq with interac:on Y=β0+β1X When Z=0 (war) Hence β1 captures the effect one- unit change of X on Y when condi:on Z is absent Y=(β0+β2)+(β1+ β3)x When Z=1 (peace) Hence β1+ β3 captures the effect one- unit change of X on Y when condi:on Z present

28 Aid, Peace, and Development Peace (Z=1) Y=(β0+β2)+(β1+ β3)x Economic Growth War (Z=0) Y=β0+β1X Level of Aid Since our hypothesis is that Development (Y) is increasing in Aid (X) if an only if Peace (Z) is present: We should expect to find β1 is zero and that β1 + β3 is posi:ve. Hence β3 should be posi:ve

29 Graph Interac:ons Same logic of graphing/ visualizing effects Once you have βs just use rules we discussed

30 OLS: DV=Development Aid 0.003*** (0.001) Peace 1.067*** (0.045) Aid*Peace 2.234*** (0.987) Constant 0.075*** (0.023) N 5672 R Expected Dev. Expected Dev. Level Aid if War if Peace Y=β0+β1X Y=(β0+β2)+(β1+ β3)x (0,075)+(0,003*AID) (0,075+1,067)+(0,003+2,234)*AID 0,105 23, ,12 34, ,135 45, ,15 57, ,165 68, ,18 79, ,195 90, ,21 101, , , ,24 124, , , ,27 146, , ,732 70

31 Same logic and Interpreta:on Dummy * Dummy = 0/1*0/1 War= Democracy*IOs Dummy* Con:nuous = 0/1*n War=Democracy*Trade Con:nuous * Con:nuous= n*n War=Democracy Index*Trade

32 Aid, Peace, and Development Peace (Z=1) Y=(β0+β2)+(β1+ β3)x Economic Growth War (Z=0) Y=β0+β1 Level of Aid We should expect to find β1 nega:ve. and that β1 + β3 is posi:ve. Hence β3 should be posi:ve and larger than β1.

33 Wrong Interpreta:on as Uncondi:onal Y=β0+β1X+β2 Z+ β3xz Effect! Development=β0+β1Aid+β2 Peace+ β3aid*peace β1 is not change of Y given one- unit change of X β1 is change of Y give one- unit change of X when Z=0!!!

34 Brambor, T., Clark, W. R., & Golder, M. (2007). Are African party systems different?. Electoral Studies, 26(2),

35 Ruggeri, Andrea, Theodora- Ismene Gizelis, and Han Dorussen. "Managing Mistrust An Analysis of Coopera:on with UN Peacekeeping in Africa." Journal of Conflict Resolu-on 57.3 (2013):

36 References Brambor, Thomas, William Roberts Clark, and Mav Golder Understanding Interac:on Models: Improving Empirical Analyses. Poli+cal Analysis 14 (1): King, Gary, Michael Tomz, and Jason Wivenberg Making the Most of Sta:s:cal Analyses: Improving Interpreta:on and Presenta:on. American Journal of Poli+cal Science, Kastellec, Jonathan P, and Eduardo L Leoni Using Graphs instead of Tables in Poli:cal Science. Perspec+ves on Poli+cs 5 (04): Ward, Michael D, Brian D Greenhill, and Kris:n M Bakke The Perils of Policy by P- Value: Predic:ng Civil Conflicts. Journal of Peace Research 47 (4):