1. DON’T WRITE DOWN THE MATERIAL ON THE FOLLOWING SLIDES, JUST LISTEN TO THE DISCUSSION AND TRY TO INTERPRET DIAGRAMS AND STATISTICAL RESULTS.

2. Social Science Models What elements (at least two) are necessary for a “social science model”?

3. Why Regression? - 1 Measures of Association (e.g., correlation) only tell us the strength of the relationship between X and Y, NOT the MAGNITUDE of the relationship. Regression tells us the MAGNITUDE of the relationship (i.e., how MUCH the dependent variable changes for a specified amount of change in the independent variable).

4. Why Regression? - 2

5. California Election 2010 - 1 Correlation of the Percent of the Countywide Vote for Barbara Boxer and Jerry Brown in 2010 with the Percentage of those 25, and Older, Who Have at Least a Bachelor’s Degree in 2000 and Median Household Income in 2008. correlate boxer10 brown10 coll00 medinc08 (obs=58) | boxer10 brown10 coll00 medinc08 -------------+------------------------------------ boxer10 | 1.0000 brown10 | 0.9788 1.0000 coll00 | 0.7422 0.6885 1.0000 medinc08 | 0.6022 0.5401 0.8321 1.0000

6. Graph of.97 Correlation of Brown10 and Boxer10

7. Graph of.74 Correlation of Coll00 and Boxer10

8. Graph of -.58 Correlation of %White in 2005 and Boxer10

9. Graph of -.23 Correlation of %Senior in 2005 and Boxer10

10. California Election 2010 - 1 Given the correlations below, what should you expect in the regression table on the next slide where the dependent variable is “boxer 10” (percent of county vote for Boxer in 2010)? correlate boxer10 brown10 coll00 medinc08 (obs=58) | boxer10 brown10 coll00 medinc08 -------------+------------------------------------ boxer10 | 1.0000 brown10 | 0.9788 1.0000 coll00 | 0.7422 0.6885 1.0000 medinc08 | 0.6022 0.5401 0.8321 1.0000

12. Probit and Logit - 1 One of the assumptions of regression is that the dependent variable has an unlimited number of categories of responses. This assumption is often violated. For example, in this class the dependent variable has frequently been a percentage. If we are not using decimals, there are 101 possible values (i.e., 0 plus 1 through 100).

13. Probit and Logit - 2 Having 101 options in the dependent variable is not a serious violation of the assumption of an unlimited number of options in the dependent variable. However, having less than 7 options is a serious violation. The “basic rule” is that if the dependent variable has fewer than 6-7 options, we should not use regression.

14. Visualizing Why We Need Probit or Logit - 1

15. Visualizing Why We Need Probit or Logit - 2

16. Visualizing the Estimation of Probit and Logit Coefficients

17. Probit and Logit - 3 Fortunately, probit and logit provide the many advantages of regression discussed in the readings in situations where the dependent variable has very few options. This situation occurs frequently in political science (e.g., in an international dispute war either broke out or did not – i.e., two categories – a voter voted either Democratic or Republican).

18. Probit and Logit - 4 Depending upon the dataset you select for your term paper, you will use either regression or probit/logit. The choice between probit and logit is largely arbitrary (i.e., typically, either is fine). The following two examples are from the vast quantitative literature in international relations.

19. Probit – International Relations-1 Major powers have frequently been in conflict over a small nation that is aligned with one of the major powers. For example, suppose China threatened to invade the Philippine Islands. In this case, the United States would be the “defender,” China the “attacker” and the Philippine Islands the “protégé” of the United States.

20. Probit – International Relations-2 The dependent variable in the ensuing analysis, “outcom” can assume only two values: 1 – deterrence succeeded – i.e., the potential attacker decided not to attack the smaller nation in question (called the “protégé”) or 0 – the potential attacker did attack and, hence, deterrence failed.

21. Probit – International Relations-3 Even if the defender defeated the attacker in an ensuing war, deterrence still “failed” because the attacker wasn’t deterred (i.e., the attacker did attack – regardless of whether the attacker “won” or “lost” the war). The following analysis is based on a dataset of 58 cases where a protégé was threatened by a major power.

22. Probit – International Relations-4 Dependent Variable: outcom: 1 = success – i.e., the potential attacking major power did not attack – deterrence was successful; 0 = failure – the potential attacker did attack – i.e., deterrence failed.

23. Probit – International Relations-5 The independent variables focus either on the value of the protégé (i.e., the more valuable the protégé the more likely the attacker will attack – that deterrence will “fail”) and the military capability of the defender (i.e., the greater the military capability of the defender the less likely the attacker will attack).

24. Probit - International Relations-6 Independent Variables: min: 1 = protégé possesses strategic minerals; 0 = protégé does not possess strategic minerals vppa: population size of the protégé nw: 1 = defender possesses nuclear weapons; 0 = defender does not possess nuclear weapons

25. Probit – International Relations-7 Stata Results: Probit regression Number of obs = 58 LR chi2(3) = 4.44 Prob > chi2 = 0.2180 Log likelihood = -37.117926 Pseudo R2 = 0.0564 ------------------------------------------------------------------------------ outcom | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- min |.2262716.4030383 0.56 0.575 -.563669 1.016212 vppa | -3.34e-06.0000106 -0.31 0.753 -.0000241.0000174 nw |.8850076.4425516 2.00 0.046.0176224 1.752393 _cons | -.0085785.2693801 -0.03 0.975 -.5365538.5193968 ------------------------------------------------------------------------------ Probit coefficients don’t directly yield the magnitude of change but they tell the direction and statistical significance of the relationship.

26. Probit – International Relations-8 How disputes are solved has frequently been a topic of quantitative studies in international relations. In the study ahead, the dependent variable is the number of times a nation was the first to use force during a dispute with another nation. Both nations receive scores on the dependent variable. The scores range from 0 to 2. Hence, probit is used.

27. Probit – International Relations-9 If a nation is the first to use a minor level of force (commit up to 1,000 troops to a combat zone) and the first to escalate the crisis to a major level (commit more than a 1,000 troops to a combat zone), then that nation receives a score of “2.”

28. Probit–International Relations-10 Alternatively, if one nation is the first to escalate a crisis to a low level of force while the other nation is the first to escalate to a high level of force, both nations receive a score of “1.” Finally, if neither nation uses military force, each nation receives a score of “0.”

29. Probit–International Relations-11 Independent variables include the level of democracy of each nation (higher scores mean greater democracy), the balance of military power between the two nations (0 to 1: scores >.50 indicate the nation has greater military capability than it’s opponent), shared alliance ties (coded “1” if the two nations share a defense alliance, “0” if not) and

30. Probit–International Relations-12 satisfaction with the status quo (based upon policy statements the nation made prior to the dispute – coded “1” if satisfied, “0” if not satisfied).

31. Probit–International Relations-13 Results: Coefficient St. Error Actor’s Democracy -.013.009 Actor’s Democracy x Opponent’s -.057.018 Democracy Opponent’s.027.009 Democracy (“x” signals an interaction term)

32. Probit–International Relations-14 Results: Coefficient St. Error Balance of Forces.996.192 Shared Alliance -.072.142 Satisfaction with -1.892.183 Status Quo What do these results tell you?

33. Probit – State Adoption of TRAP Abortion Laws DON’T WRITE THE NUMBERS! Ind. Var. Coefficient St. Error Dem. Control -.555.260 State Ideology.003.010 % Catholic.009.010 % Fundamental.029.009 Public Opinion -.825.465 about Abortion

34. Probit – State Adoption of an Income Tax Over 1916-1937 DON’T WRITE THE NUMBERS! Ind. Var. Coefficient St. Error Liberal Control.788.318 Real Per Capita -1.802.892 Income Governor -.925.301 Election Year

35. Probit – Issues and Voting - 1 In the ensuing analysis the dependent variable (the probability of voting Democratic for President) has only two categories of responses (the voter either voted Democratic for President – coded as “1”, or did not vote Democratic for President - coded “0”). Therefore, we will use probit instead of regression.

36. Probit – Issues and Voting - 2 The independent variables are the voter’s position on various policy oriented scales. The voter’s responses to each of the policy questions are coded -1, 0, or +1. The more liberal the answer the higher the score.

37. For example, since liberals support government services and typically want to spend less on defense, a respondent who wanted the government to provide many more services and increase spending a lot was coded “1” (0 = keep the same, -1 decrease a lot) Probit – Issues and Voting - 3

38. Probit – Issues and Voting - 4 while those wanting to decrease military spending a lot were also coded “1” (0 = keep the same, -1 increase spending a lot). Do the results on the next slide support the view that social issues have replaced economic issues as the prime issue basis of voting?

39. Probit – Issues and Voting - 5 High Low Income Voters Income Voters Govt. services 1.08 (.10).52 (.17) Defense spending 1.00 (.14).83 (.15) Govt. jobs.52 (.05).31 (.08) Abortion.47 (.10).23 (.10) Aid to Blacks.35 (.11).18 (.08) Women’s Role.25 (.07).33 (.08) Note the relative size of the coefficients