Binary Choice. Multiple Choice. LPM logit logistic regresion probit. Multinomial Logit
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1 (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 3 Bary Choc LPM logt logstc rgrso probt Multpl Choc Multomal Logt (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 4
2 Not that Pr(choc# j j fucto F j ( must rtur a valu btw 0 ad (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 5 (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 7 Qusto: What dtrms th choc slcto? Modl to dtrm th probablty of a vt udr a gv codto (valu of dpdt varabls Pr(choc#jF j (,,, whr s ar dtrmats for th probablty. (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 6 Exampl JOIN f th obsrvato wll jo th govrmt-ru halth surac program 0, othrws (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 8
3 JA f th obsrvato wll jo Pla A 0, othrws JB f th obsrvato wll jo Pla B 0, othrws JC f th obsrvato wll jo Pla C 0, othrws Not that JA+JB+JC always. (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 9 Df Assumpto of LPM Larty of F(. P Pr( JOIN P + + L+ Not that thr s o rror trm (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty Gral Structur Pr( JOIN F(,,..., Not that (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty Pr( JOIN 0 F(,,..., 0 F(,,..., 0 Formulato of LPM E(JOIN(P+(0(-PP > JOINP+v whr v s a rror trm. E(v0 JOIN + + L+ + v > OLS s vald but ot th bst. Why? (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty (
4 Not that V(ν V(JOIN but V(JOIN (-P P+(0-P (-P P(-P > V(ν s ot costat. It dpds o th dpdt varabls ( s > Volato of a CLRM assumpto or ν s htroscdastc (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 3 Not that V ( ν w V ( ν P( P P( P > OLS s BLUE for Modl ( (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 5 Df JOIN whr w P( P + + L+ JOIN w ν wν + ν wjoin (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty for (,..., 4 Estmato of LPM Stp ru OLS for uwghtd modl ( > JOIN Not that JOIN s th stmat for P (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 6
5 Stp comput th wght w JOIN ( JOIN Stp 3 comput JOIN,,,..., Stp 4 stmat th wghtd modl ( usg OLS (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 7 Corrcto If <0, st JOIN0 If >, st JOIN (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 9 Stp 5 r-comput JOIN usg th w st of. Not that LPM dos ot assur that P 0 JOIN or 0 F(,,..., (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 8 (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 0
6 Lss xpsv computr tm. No o-lar quatos P s th ffct of o th probablty. I gral, th xplaatory varabls should b utlss or ar xprssd prctag Z Z (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 3 Assumpto of Logt F( s a logstc fucto P Z + Z + + L+ Not that 0 F( Z (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty always. No rror trm Not that OLS dos ot apply ML Estmato of Logt modl or max L max l L Not that YJOIN ( P Y ( P (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty ( Y [ Y l( P + ( Y l( P ] 4
7 Not that P Frst-ordr codtos For,, l L [ [ Z Y + + Z Z Z ( Y + (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty ] Z ] 0 5 Varac-Covarac Matrx for l L V ( ˆ j Not that t s ot th stmatd VC matrx. Do Z-tst or Ch-squar tst stad of t- tst or F-tst o paramtrs (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty ˆ 7 Solvg FOC for ML stmats. Scod-ordr Codtos l L j [ [ ( Y (+ Z Z ylds Varac-covarac matrx of j j Z Y (+ Z ] ] ˆ Itrprtato P (+ Z Z } { + sg of >drcto of th ffct of o th probablty to JOIN. (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 6 (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 8
8 No R for a logt modl sc thr s o rror trm. Df # corrct prdcto psudo R sampl sz ( It s a masur for goodss-of-ft. JOIN>0.5 > prdct that JOIN JOIN<0.5 > prdct that JOIN0 From Logt Modl l P P + + L+ Not that P s th xpctd proporto of populato JOINg gv s (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 9 (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 3 Assumpto of Logstc Rgrsso F(. s a logstc fucto but th obsrvato(xprmt for ach gv st of dpdt varabls ( wll b rpatd svral tms. Oly th proporto of JOIN ca b obsrvd. (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 30 Df R obsrvd proporto of obsrvato wth th sam valu of that JOIN. Drvd Modl R l ν R L V ( ν Why? N R ( R (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 3
9 Df Estmato whr R w N R ( R R R w l R w ν wν (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty ν for,..., 33 Assumpto of Probt F( s a cumulatv dstrbuto fucto of a stadard ormal. Z + + L+ Not that PΦ( Z 0 Φ( Z (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty No rror trm always. 35 > OLS s BLUE Itrprtato of th paramtrs sam as thos for logt modl as th udrlyg fucto s also logstc Φ(Z Z Z (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 34 (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 36
10 Assumpto of Multomal Logt Df PA Pr(JA PB Pr(JB PC Pr(JC Choos th choc of pla C as th rfrc. PA + PB PC PA + PB + PC PC (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 37 (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 39 whr whr PA PC α + α + L+ α PB PC + + L+ PA PB (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 38 (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 40
11 ML Estmato of Multomal Logt modl max L or max l L ( PA + ( JA Solvg FOC ylds JA ( PB [ JA l( PA + JB (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty JB ( PA PB l( PB JB l( PA αˆ, ˆ ( JA JB PB ] 4 Itrprtato PA + + PA ( PA α PA PB ow-ffct cross-ffct sg of α >drcto of th ow-ffct of o th probablty to JOIN A. sg of >drcto of th cross-ffct of o th probablty to JOIN A. (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 43 Itrprtato PA α + + ( α + ( α (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 4 Nstd Logt /Sral Logt Ordrd Logt Gralzd Extrm-Valu (GEV (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 44
12 Modls for Lmtd Dpdt Varabls Csord Rgrsso Tobt Modls (c Pogsa Porchawssul, Faculty of Ecoomcs, Chulalogor Uvrsty 45
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