F^3: F tests, Functional Forms and Favorite Coefficient Models

Transcription

1 F^3: F tests, Functional Forms and Favorite Coefficient Models Favorite coefficient model: otherteams use "nflpricedata Bdta", clear *Favorite coefficient model: otherteams reg rprice pop pop2 rpci wprcnt1 po5 otherpro cap95 newstad tempstad exp reloc Source SS df MS Number of obs = F(11, 587) = 3868 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = rprice Coef Std Err t P>t [95% Conf Interval] pop pop rpci wprcnt po otherpro cap newstad tempstad exp reloc _cons *F tests: *-testing one parameter and t-tests test pop ( 1) pop = 0 F( 1, 587) = 2731 Prob > F = di sqrt(2731) test exp ( 1) exp = 0 F( 1, 587) = 209 Prob > F = di sqrt(209)

2 *-testing joint hypotheses (multiple parameters) test (pop=0) (pop2=0) ( 1) pop = 0 ( 2) pop2 = 0 F( 2, 587) = 2705 Prob > F = test pop pop2 ( 1) pop = 0 ( 2) pop2 = 0 F( 2, 587) = 2705 Prob > F = test wprcnt1 po5 ( 1) wprcnt1 = 0 ( 2) po5 = 0 F( 2, 587) = 2003 Prob > F = * and functional forms: reg rprice pop pop2 yr Source SS df MS Number of obs = F(3, 595) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = rprice Coef Std Err t P>t [95% Conf Interval] pop pop yr _cons gen yr2=yr^2 2

3 reg rprice pop pop2 yr yr2 Source SS df MS Number of obs = F(4, 594) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = rprice Coef Std Err t P>t [95% Conf Interval] pop pop yr yr _cons reg rprice pop pop2 iyr Source SS df MS Number of obs = F(20, 578) = 2090 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = rprice Coef Std Err t P>t [95% Conf Interval] pop pop yr _cons predict yhat (option xb assumed; fitted values) scatter yhat pop 3

4 pop test iyr i: operator invalid r(198); *OOPS! let's try that test a different way testparm iyr ( 1) 1997yr = 0 ( 2) 1998yr = 0 ( 3) 1999yr = 0 ( 4) 2000yr = 0 ( 5) 2001yr = 0 ( 6) 2002yr = 0 ( 7) 2003yr = 0 ( 8) 2004yr = 0 ( 9) 2005yr = 0 (10) 2006yr = 0 (11) 2007yr = 0 (12) 2008yr = 0 (13) 2009yr = 0 (14) 2010yr = 0 (15) 2011yr = 0 (16) 2012yr = 0 (17) 2013yr = 0 (18) 2014yr = 0 F( 18, 578) = 1422 Prob > F =

5 *Dummies capture average residuals (what your model did not otherwise explain): reg rprice pop pop2 iyr Source SS df MS Number of obs = F(20, 578) = 2090 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = rprice Coef Std Err t P>t [95% Conf Interval] pop pop yr skip a few _cons gen resid = rprice - ( *pop *pop2) tabstat resid, by(yr) stat(mean) yr mean e skip a few Total

6 *Bring on the dummies team quality effects: xi iteam iteam _Iteam_1-32 (_Iteam_1 for team==arizona omitted) reg rprice wprcnt1 po5 iyr _I* Source SS df MS Number of obs = F(51, 547) = 1998 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = rprice Coef Std Err t P>t [95% Conf Interval] wprcnt po yr _Iteam_ _Iteam_ _Iteam_ _Iteam_ _cons margins, eyex(wprcnt1 po5) atmeans Conditional marginal effects Number of obs = 599 Model VCE : OLS Expression : Linear prediction, predict() ey/ex wrt : wprcnt1 po5 Delta-method ey/ex Std Err t P>t [95% Conf Interval] wprcnt po

7 *Polynomials: reg rprice pop Source SS df MS Number of obs = F(1, 597) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = rprice Coef Std Err t P>t [95% Conf Interval] pop _cons predict phat1 (option xb assumed; fitted values) reg rprice pop pop2 Source SS df MS Number of obs = F(2, 596) = 5797 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = rprice Coef Std Err t P>t [95% Conf Interval] pop pop _cons predict phat2 (option xb assumed; fitted values) gen pop3=pop^3 7

8 reg rprice pop pop2 pop3 Source SS df MS Number of obs = F(3, 595) = 3863 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = rprice Coef Std Err t P>t [95% Conf Interval] pop pop pop _cons predict phat3 (option xb assumed; fitted values) scatter phat* pop pop vif Variable VIF 1/VIF pop pop pop Mean VIF

9 test pop2 pop3 ( 1) pop2 = 0 ( 2) pop3 = 0 F( 2, 595) = 666 Prob > F = *So drop one of the two pop variables, but not both! *Percentile dummies here, quintile dummies xtile pop5=pop, n(5) scatter pop5 pop (below) reg rprice ipop5 Source SS df MS Number of obs = F(4, 594) = 2911 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = rprice Coef Std Err t P>t [95% Conf Interval] pop _cons predict phat5 (option xb assumed; fitted values) scatter phat2 phat5 pop 5 quantiles of pop pop pop 9

10 *Use areg to run fixed effect but only for one variable: reg rprice ipop5 rpci wprcnt1 po5 otherpro cap95 newstad tempstad exp reloc Source SS df MS Number of obs = F(13, 585) = 2830 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = rprice Coef Std Err t P>t [95% Conf Interval] pop rpci wprcnt po otherpro cap newstad tempstad exp reloc _cons areg rprice rpci wprcnt1 po5 otherpro cap95 newstad tempstad exp reloc, absorb(pop5) Linear regression, absorbing indicators Number of obs = 599 F( 9, 585) = 2352 Prob > F = R-squared = Adj R-squared = Root MSE = rprice Coef Std Err t P>t [95% Conf Interval] rpci wprcnt po otherpro cap newstad tempstad exp reloc _cons pop5 F(4, 585) = (5 categories) 10

11 *Why hold back after all, it's a favorite coefficient model! xtile rpci5=rpci, n(5) reg rprice ipop5 irpci5 wprcnt1 po5 otherpro cap95 newstad tempstad exp reloc Source SS df MS Number of obs = F(16, 582) = 2456 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = rprice Coef Std Err t P>t [95% Conf Interval] pop rpci wprcnt po otherpro cap newstad tempstad exp reloc _cons xtile wprcnt5=wprcnt1, n(5) reg rprice ipop5 irpci5 iwprcnt5 po5 otherpro cap95 newstad tempstad exp reloc Source SS df MS Number of obs = F(19, 579) = 2100 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = rprice Coef Std Err t P>t [95% Conf Interval] pop rpci

12 wprcnt po otherpro cap newstad tempstad exp reloc _cons reg rprice ipop5 irpci5 iwprcnt5 ipo5 otherpro cap95 newstad tempstad exp reloc Source SS df MS Number of obs = F(23, 575) = 1814 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = rprice Coef Std Err t P>t [95% Conf Interval] pop rpci wprcnt po otherpro cap newstad tempstad exp reloc _cons

13 * Run a few tests, will ya? testparm ipop5 ( 1) 2pop5 = 0 ( 2) 3pop5 = 0 ( 3) 4pop5 = 0 ( 4) 5pop5 = 0 F( 4, 575) = 443 Prob > F = testparm ipop5 irpci5 ( 1) 2pop5 = 0 ( 2) 3pop5 = 0 ( 7) 4rpci5 = 0 ( 8) 5rpci5 = 0 F( 8, 575) = 2074 Prob > F = testparm ipop5 irpci5 iwprcnt5 ( 1) 2pop5 = 0 ( 2) 3pop5 = 0 ( 8) 5rpci5 = 0 ( 9) 2wprcnt5 = 0 (10) 3wprcnt5 = 0 (11) 4wprcnt5 = 0 (12) 5wprcnt5 = 0 F( 12, 575) = 1540 Prob > F =