Addressing Alternative Explanations: Multiple Regression
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1 Addressng Alternatve Explanatons: Multple Regresson 7.87
2 Dd Clnton hurt Gore example Dd Clnton hurt Gore n the 000 electon? Treatment s not lkng Bll Clnton How would you test ths?
3 Bvarate regresson of Gore thermometer on Clnton thermometer Clnton thermometer
4 Dd Clnton hurt Gore example What alternatve explanatons would you need to address? Nonrandom selecton nto the treatment group (dslkng Clnton from many sources Let s address one source: party dentfcaton How could we do ths? Matchng: compare Democrats who lke or don t lke Clnton; do the same for Republcans and ndependents Multvarate regresson: control for partsanshp statstcally
5 Democratc pcture Clnton thermometer
6 Independent pcture Clnton thermometer
7 Republcan pcture Clnton thermometer
8 Combned data pcture Clnton thermometer
9 Combned data pcture wth regresson: bas! Clnton thermometer
10 Combned data pcture wth true regresson lnes overlad Clnton thermometer
11 Temptng yet wrong normalzatons Subtract the Gore therm. from the avg. Gore therm. score Clnton thermometer Subtract the Clnton therm. from the avg. Clnton therm. score Clnton thermometer
12 3D Relatonshp
13 The Lnear Relatonshp between Three Varables Gore thermometer Clnton thermometer Party ID Y 0,,
14 Multvarate slope coeffcents Bvarate estmate: Multvarate estmate: B M Clnton effect (on Gore n bvarate (B regresson cov(, Y var( cov(, Y var( vs. - M Party ID effect (on Gore n multvarate (M regresson cov(, var( Clnton effect (on Gore n multvarate (M regresson B M cov(, var( M When does? Obvously, when 0 Clnton effect on Party ID n bvarate regresson
15 The Slope Coeffcents n n n n n n n n Y Y Y Y,,,,,,,,,, ( ( ( - ( ( ( and ( ( ( - ( ( ( s Clnton thermometer, s PID, and Y s Gore thermometer
16 The Slope Coeffcents More Smply var(, cov( - var(, cov( and var(, cov( - var(, cov( Y Y s Clnton thermometer, s PID, and Y s Gore thermometer
17 The Matrx form y y x, x, x k, x, x, x k, y n x,n x,n x k,n ( y
18 3D Lnear Relatonshp
19 The Output. reg gore clnton party3 Source SS df MS Number of obs = F(, 74 = Model Prob > F = Resdual R-squared = Adj R-squared = Total Root MSE = gore Coef. Std. Err. t P> t [95% Conf. Interval] clnton party _cons Interpretaton of clnton effect: Holdng constant party dentfcaton, a onepont ncrease n the Clnton feelng thermometer s assocated wth a.5 ncrease n the Gore thermometer.
20 Separate regressons ( ( (3 Intercept Clnton Party
21 Is the Clnton effect causal? That s, should we be convnced that negatve feelngs about Clnton really hurt Gore? No! The regresson analyss has only ruled out nonrandom selecton on party ID. Nonrandom selecton nto the treatment could occur from Varables other than party ID, or Reverse causaton, whch s feelngs about Gore nfluencng feelngs about Clnton. Addtonally, the regresson analyss may not have entrely ruled out nonrandom selecton on party ID because t may have assumed he wrong functonal form. E.g., what f nonrandom selecton on strong Republcan/strong Democrat
22 Summary: Why we control Address alternatve explanatons by removng confoundng effects Improve effcency
23 Why dd the Clnton Coeffcent change from 0.6 to 0.5. corr gore clnton party, cov (obs=745 gore clnton party gore clnton party
24 The Calculatons B cov( gore, clnton var( clnton M cov( gore, clnton var( clnton M cov( clnton, party var( clnton. corr gore clnton party,cov (obs=745 gore clnton party gore clnton party
25 Accountng for total effects M M M B M M B M M Y - var(, cov( - var(, cov(
26 Accountng for the total effect B M M Total effect = Drect effect + ndrect effect M Y M
27 Accountng for the total effects n the Gore thermometer example Effect Total Drect Indrect Clnton Party
28 Other approaches to addressng confoundng effects? Experments Dfference-n-dfferences desgns Others? Is regresson the best approach to addressng confoundng effects? Problems
29 Drnkng and Greek Lfe Example Why s there a correlaton between lvng n a fraternty/sororty house and drnkng? Greek organzatons often emphasze socal gatherngs that have alcohol. The effect s beng n the Greek organzaton tself, not the house. There s somethng about the House envronment tself.
30 Dependent varable: Tmes Drnkng n Past 30 Days
31 . nfx age 0- resdence 6 greek 4 screen 0 tmespast30 03 howmuchpast30 04 gpa studyng 8 tmeshs 35 howmuchhs 36 socalzng 83 stwgt_ weght usng da388.dat,clear (438 observatons read. recode tmespast30 tmeshs (=0 (=.5 (3=4 (4=7.5 (5=4.5 (6=9.5 (7=45 (tmespast30: 657 changes made (tmeshs: 07 changes made. replace tmespast30=0 f screen<=3 (463 real changes made
32 . tab tmespast30 tmespast30 Freq. Percent Cum , , , , , Total 3,
33 Three Regressons Dependent varable: number of tmes drnkng n past 30 days Lve n frat/sor house 4.44 ( (0.38 Member of frat/sor ( (0.8 Intercept 4.54 ( ( (0.059 R N 3,876 3,876 3,876 Note: Corr. Between lvng n frat/sor house and beng a member of a Greek organzaton s.4
34 The Pcture 0.9 Lvng n frat house.6 Drnks per 30 day perod Member of fraternty.44
35 Accountng for the effects of frat house lvng and Greek membershp on drnkng Effect Total Drect Indrect Member of Greek org. Lve n frat/ sor. house (85% (5% 0.44 (5%.8 (49%
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