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1 Logistic CJS 35 : 洪岩璧 : Logistic,, Logistic ( ),,, y* KHB (APE) (LPM), CGSS2006,,, :Logistic OntheCoefficientsComparisonbetweenLogisticRegressions andthesolutions:abriefreview HONG Yanbi DOI: /j.cnki /c Abstract:ThispaperintroducedthecoefficientscomparisonbetweenLogistic regresion,whichincludescomparisonbetween modelswithinsampleandthat betweensamplesorsubsamples.duetotheunobservedheterogeneity ( residual variation) p roblem inlogistic models,itisinappropriatetofolow the OLS coefficientscomparison in a naivesimple way.with the same dependent * : (Author:HONG Yanbi,Departmentof Sociology, SchoolofHumanities,SoutheastUniversity ) hongyb@seu.edu.cn ** 2011, ( S30026) [ThispaperissupportedbyTheCo-InnovationCenterofCivilMoralityandSocialCustom, ResearchCenterofNationalMoralSurvey, and thefundamentalresearchfundsforcentral Universities ( S30026).] (CGSS)2006, 220

2 Logistic : variable,thetotalvarianceofolsregresionfunctionisalwaysfixed,whichis irrelevanttothenumberofindependentvariables.however,thetotalvarianceof Logisticregresionfunctionwilchangeastheindependentvariablesincreaseor decrease,becausethevarianceoferrorinlogisticregresionisasumedtobe constant,equals π 2 /3.Previousresearchersproposed manysolutionstothis comparison problem.based on the literature,this paper introduced five solutions: y *-standardization,khbdecomposition,heterogeneouschoicemodel, average partialeffect (APE),and linear probability model (LPM ).Y * - standardizationand KHB only workin comparison between models within sample,heterogeneouschoicemodelonlyworksincomparisonbetweensamples orsubsamples,andapeandlpm workinbothsituations.drawinguponcgss 2006data,usingeducationaltransition modelasanexample,theauthorthen showedtheuseandthedifferencesbetweenthefivesolutionsthroughexamining thecohortdifferencesinschooltransitionand whethertheeffectsofparental ISEIdifferintwocohorts schooltransition.thefinalpartsummarizedthe characteristicsandcontextsofthefivesolutions. Keywords:Logisticmodels,coefficientscomparison,unobservedheterogeneity, residualvariation Logistic, ( ) ( ) ( ) ( ), Logistic,,, ; ( ), 1 (log-oddsratio,lnor) (oddsratio,or) 2 1., 2. (2010: ) oddsratio, (1999), odds, oddsratio 221

3 Logistic :, (OLS) ;, (HosmerandLemeshow,2000:X),, Logistic,3 Logistic, 1984, (Winshipand Mare,1984),, (Alison,1999), Logistic, ( ), Logistic, OLS Logistic, Logistic,, Logistic, Logit ( OrdinalLogit MultinomialLogit ) Probit, Logistic Logistic, ;, y* KBH (APE) (LPM) ;, : Logit ( ), Logit (,2014;WangandXie,2015) Logistic, (Mood,2010), 3. (1999) (2010), (2009:30-35) (2012: ) 222

4 Logistic : (unobservedheterogeneity ), (omitedvariables) 4, 0,,, Logistic, 1( ) 0( ),, y * y * >0, y = 1; y * 0, y =0 5 y * 1, OLS, y * 1, y*, 2, ( ), y,, y *, (unidentified)(longandfreese,2001:102) 6, yi ( ), βk, (,2010:340) Logistic, Logistic, 0, π 2 /3, ,, 4. (residualvariation) Probit, (Wooldridge,2002: ) 5. (transformation) (, 2009) 6.,,,, (,2012:26-27) 7. Probit, 0, 1 (LongandFreese,2001: ) 223

5 2015 4, ( ),b 1 b 1 x 1, y * i =α+x 1iβ 1 +εi (1) [ ] ln P (2) 1-P =a+x1ib1 2 Logit, (log odds), 1 3: y * i =α+x 1iβ 1 +σεi (3) 1, 3 σεi, εi π 2 /3 =3.29, σ, σ, εi, Logistic 2 b 1 β/σ( 3 σ), 1 β 1 8, β, 1 Logistic, 3.29 Logistic, (omitedvariable)x 2 4 : y i * =α+x 1iβ 1 +x 2iβ 2 +σεi (4),εi Logistic, 3.29( σ 1) x 1 x 2 5 : x 2i =γ0 +γ1x 1i +v i (5) γ0 γ1,v i 4 εi 4 x 2,, 5 4, x 1 β 1+β, 2γ1 x 2 β 1 x , (Mood,2010),Logistic,, ( partial effect),,β/σ β (Wooldridge,2002:470;Cramer,2007) Logit,β/σ 9. x1 x2, 224

6 Logistic :,σ=1, 3.29, b 1 β/σ=β ; 1 1 x 2, var(ε)+β 2 2 var(v), σ = 槡 3.29+β 2 2 var(v )/ 槡 3. 29, 4 x 2, b 1 6 : β 1, b 1 = ( β 1 +β )[ 槡 2γ / 槡 3.29+β 2 2var(v )] (6) x 1 x 2, 6 : b 1 =β [ 槡 / 槡 3.29+β 2 2var(x 2 )] (7),, (omited-variablebias), (,2010:105), Logistic,, 7, ( ), [var(x 2 )] y ( β 2 ),10 2,, β2var(v), 7,,, σ >1, (Wooldridge,2002:470), Logistic, Logistic, :,,, 10., R 2, 225

7 2015 4,,,, ( 一 ) 同一样本, 不同模型之间的系数比较,, Logistic, (Karlson,etal.,2013), (confounding ) (rescaling ) 3 4 (, 3a 4a ), ( R) ( F) 11 x 1 x 2, x 2 y *,, x 1,,, y * i =x 1iβ 1R +σrεi (3a) y * i =x 1iβ 1F +x 2iβ 2 +σfεi (4a) b 1R -b 1F = β1r σr - β1f σf β 1R - β 1F (8),b β,, σr σf 8,, 1. y* y* ( y * -standardization) 12 (Winshipand Mare,1984:517), 11. (2010:138) 12. (2012:327) y *, y 226

8 Logistic :, SD( y* ), SD(y*)= 槡 var(x b)+var(ε )= 槡 var(x b) (9) 9 (Karlson,etal.,2013:298;Long, 1997:129), SD( y* ) : ; (3.29), SD( y* ),,,, y* y *, b/sd( y* ),, y * (standard-deviation-unitchangeiny * ) 13, y*, Stata, Logit listcoef,stdhelp, y * (LongandFreese,2001:155) 2.KHB (Karlson,etal.,2013) KHB x 2 x 1 珟 x 2, 5 v i 珟 x 2 x 2 4a, 10 3a 4a 10, β 1R =β 1F * σf =σ F * 14 y i * * =x 1iβ 1F + 珟 * x 2iβ 2 +σ Fεi * (10) (Karlson,etal., 2013:292),,, 珟 x 2 x 2 x 1, 珟 x 2 x 1, 珟 x 2 x 1, 珟 x 2 x 2 x 1, (2010:105) 13., (,2012:327) 14. (2010: ) 227

9 2015 4, β 1R = β 1F *,, 4a 10 4a x 1 y * x 2, x 2 y * x 1 10 x 1 y *, x 2 x 1 ( 珟 x 2 ) y *, x 2 x 1 y * x 1 y * 4a 10 x 1 x 2 y *, 4a 10, σf =σ F *, 4a 10 4a 10, *,, β 1F β 1F (Karlson,etal.,2013) : (1) : b 1F * -b 1F = β* 1F - β1f σ F * σf (2) : = β1r - β1f = ( β 1R - β ) 1F σf σf σf (11a) b 1F = β1f /σf = β1f b 1F * β * 1F/σ F * β 1R (3) : (11b) b * 1F -b 1F = ( β 1F * -β 1F )/σf = - β1r β 1F 100% (11c) b * 1F β * 1F/σ F * β 1R,, (11a), Logit (11b) (11c),, Logit, 12,b 1F * -b 1F, b 1R -b * 1F = β1r σr - β1r σf 228

10 Logistic : b 1R -b 1F = β1r σr - β1f σf = β1r σr - β* 1F σ * F + β* 1F - β1f σ F * σf = (b 1R -b * 1F)+ (b * 1F -b 1F ) (12) (Karlson,etal.,2013) Z C, Logit, y* APE LPM,KHB, Stata khb 15 ( 二 ) 同一模型, 不同组别或样本之间的系数比较 Logistic,, (indicatorvariable),, Wald ( ), 13 (Clogg, Petkovaand Haritou, 1995), β 1i β 2i,SE( β 1i) SE( β 2i), β 1i - β 2i (13) 槡 SE 2 ( β 1i)+SE 2 ( β 2i ),,, (2010:239) Logit,, (Alison,1999), (1999:157),,, 15. khb :htp :// fmwww.bc.edu/repec/bocode/k/khb.html, (Kohler,KarlsonandHolm,2011) 229

11 ,,,,, ( ),, Logit, σ ( 3 4 ), σ, ( ),, (residualvariation) (Hoetker,2004),, ( ) Logit,,, (Alison,1999) ( ), Logistic, 2,, σ (σf >σm ), 7,b=β / σ,, β F β M, b F b M,, (Alison,1999) Logistic, :, ;, (Wiliams,2009:546),, (Alison,1999)

12 Logistic : :,,, (Alison, 1999) 1. (heterogeneouschoicemodel) (Wiliams,2009) Logit, (Alison,1999) (HauserandAndrew,2006) Logistic (location-scale model), (heteroscedasticiy ), ( ), Logit ; ( ),,,, 14 ( ): [ ] [ ] Pr(yi =1)=g xi β exp(z iγ ) =g x iβ exp(ln(σi )) =g ( xi β) (14) σi,g ( Logit, Probit Complementarylog-log Log-log Cauchit) x i, x z i, z z,,z x 17 β γ, x z ( σ ) 14,,, 17.,,z Stata oglm stepwise, 231

13 Logit, ( ), (Wiliams,2009), Stata oglm(ordinalgeneralizedlinearmodel) (Wiliams,2010) 2. (APE) Logit, (oddsratio), ( p robability ) (Petersen,1985), Logit, Logistic (CDF): F( β x i )= exp ( β x i ) 1+exp( β x i ) βx i i Logit LogisticCDF (PDF), : f( β x i )= exp ( β x i ) [1+exp( β x i )] 2 CDF yi=1 P( yi=1), P( yi=1) PDF P(yi =1) [1-P(yi =1)] Logit,, (MarginalEffects, MFX) (Average MarginalEffects, AME) (Average PartialEffects, APE) x, x (,2009:56-57) Logit x 1 (MFX) : f( β x i ) β 1 = exp ( β x i ) [1+exp( β x i )] 2β1 (15a), β 1 x 1 (logodds-ratio), β x i 232

14 Logistic : i Logit,f( β x i ) β x i Logistic (PDF) x 1,, (Mood,2010:75) (, 7 ), 0.5, P(yi =1) [1-P(yi =1)] 0.25,, (APE), (Cramer, 2007) APE 15b, x 1,, 0.01 APE,APE,,APE x 1, 1 N N i=1 f( β x i ) β 1 = N 1 N i=1 exp( β x i ) [1+exp( β x i )] 2β1 (15b) (Karlson,etal.,2013) APE KHB, APE,, Stata margeff APE, x 1 APE (LPM) (LinearProbability Model, LPM),, Logit Probit LPM Logistic,,, :,, (homoscedasticity );, (0-1), ;, 18. (Cramer,2007) ASE margeff ( ) 233

15 (,1999;,2010:332), (WeightedLeast Squares) (Heteroscedasticity-robust Standard Errors) (,2009:34;Mood,2010) [0,1], (2010:338), (Winshipand Mare,1984: 514) Logit Probit (Long, 1997),, 0 1, (Mood,2010) LPM Logit, LPM (MarginalEffect), Logit (,2003:520), LPM,, (Mood,2010), 19 (2003:519) LPM Logit Probit,, (Karlson,etal.,2013), Logit,LPM :, (Mare,1980;1981),,, 19., (2012:332), (,2014;WangandXie,2014) 234

16 Logistic : (HolmandJ ger,2011) CGSS2006,20 (ISEI), 20 39, 3132, (20 29 )1471, (30 39 )1661, 1 (ISEI), Logistic LPM( ) APE y* KHB, Logistic ( ) LPM APE OGLM ( ) 1: (N=3132) ( ) (s) (0.491) (male) (0.499) (coh) (0.499) 18 (iseif18) (16.889) 18 (iseim18) (20.136) 18 (bkn) (20.136) ( 一 ) 同期群的影响 2 Logistic Logistic, R1 F1 (coh),,coh 12.4% [( )/0.573] LPM, L1 L2 coh, 14.7% [( )/0.136], 2, y*, R1 F1 SD( y* ) CGSS2006, ( ) (,2009) 235

17 ,Beta/SD( y* ), R1 F1,coh 25.1% [( )/0.312] 2, KHB,coh 26.5%[( )/0.682] 0.683, Logistic R1 (0.573) KHB F1,21 [ y* SD( y* ) ],, F1, 2, R1 F1,coh APE 16.5%[( )/0.127], y* KHB ; Logistic, APE,,APE (Cramer,2007),,,,, Logit y * KHB,, ( 8 ),,,,,, y* KHB, ( 二 ) 父母职业地位影响在同期群间的差异 3 Logistic OGLM LPM F2, 21.,, KHB,, 236

18 Logistic : 2: Logistic LPM (N=3132) Logistic (LPM) (R1) (F1) (L1) (L2) (coh) *** *** *** *** SD( y * ) Beta/SD( y * ) (0.074) (0.078) (0.017) (0.017) KHB-coh *** *** (0.079) (0.078) APE *** *** (0.006) (0.006) 注 :1. 显著性水平 : *p<0.05, **p<0.01, ***p<0.001 括号中为标准误 ; 2. 简化模型 R1 和 L1 包含了性别变量, 完全模型 F2 和 L2 包括性别 18 岁时父亲和母亲的职业 18 岁时家庭藏书量三个变量 ; 3. 本表没有报告其他控制变量的系数估计结果, 有兴趣的读者可向作者索取,,, ( 13) 22 O2,,, 3,OGLM ( Logistic ),, ln(sigma) O1, 75.2%[exp ( )] O2,, 1999 OGLM(O2) (L3),, Logistic (F2),18, OGLM(O2) LPM(L3),, (Mood,2010),,, 4 APE Logistic (F2),,APE,, OGLM 22., Logistic 237

19 : Logistic OGLM LPM (N= 3132) Logistic (F2) OGLM (O1) (O2) LPM (L3) *** *** *** *** (0.003) (0.003) (0.003) (0.001) * *** * * (0.003) (0.002) (0.003) (0.001) *** * ** (0.205) (0.089) (0.232) (0.040) (0.006) (0.008) (0.001) * (0.004) (0.005) (0.001) / *** *** *** *** (0.136) (0.134) (0.135) (0.028) :ln(sigma) * (0.134) (0.283) (df) 409.9(7) 409.7(6) 412.1(8) BIC 注 :1. 显著性水平 : *p<0.05, **p<0.01, ***p<0.001 括号中为标准误, 模型卡方后面括号中为自由度 ; 2. 所有的模型还包括了性别和家庭藏书量 4:Logistic APE Logistic ** (0.026) (0.024) (0.007) *** *** *** (0.001) (0.001) (0.000) *** * *** (0.001) (0.001) (0.000) *** *** *** (0.001) (0.000) (0.000) * (0.018) * (0.000) *** (0.000) N 注 : 显著性水平 : *p<0.05, **p<0.01, ***p<0.001 ; 括号中为标准误 F2,, O1 238

20 Logistic :, O2 O2 F2,,, OGLM O1, F2 O2 O1 1 2, BIC, O1 BIC F1 O2,OGLM O1,,,,, (Wiliams,2009),,,, Logistic,,Logistic, Logit Probit, 5: / Stata (oddsratio) logistic,logit y * listcoef KHB khb (HCM) oglm (APE) a margeff (LPM) regres 注 :1.a: 需在不同的点取值才能体现非线性 ; 2. 本表部分内容来自穆德 (Mood,2010:80) 的表 6 5 6, 239

21 ( ), Logistic,, (Karlson,etal.,2013) y* KHB,,,,, Logistic,, (Hoetker,2004),, (References) [M].,,. :., D [M].,. : [M]. : [ J ]. (5): : [M].,. :., J.M [ M].,. : [M]. : ( )[M]. :. Alison,Paul D Comparing Logitand Probit Coefficients Acros Groups. Sociological Methods&Research28(2): Clogg, CliffordC.,EvaPetkova,andAdamantiosHaritou StatisticalMethodsfor Comparing Regresion Coefficients Between Models. The American Journal of Sociology100(5): Cramer, J.S RobustnesofLogitAnalysis:Unobserved Heterogeneityand Mis- SpecifiedDisturbances. Oxford BuletinofEconomicsandStatistics69(4): Hauser,Robert M.and Megan Andrew AnotherLookattheStratification of EducationalTransitions:The Logistic Response Model with PartialProportionality Constraints. Sociological Methodology36(1):1-26. Holm,Andersand Mads MeierJ ger Dealing withselectionbiasineducational Transition Models:The Bivariate Probit Selection Model. Research in Social Stratificationand Mobility29(3): Hoetker,Glenn Confounded Coefficients:Extending Recent Advancesin the 240

22 Logistic : AccurateComparison of Logitand Probit Coefficients Acros Groups. Working Paper,Oct.22,2004.UniversityofIlinoisatUrbana-Champaign.( asu.edu/.../research/hoetker confounded wp.pdf). Hosmer,David W.andStanleyLemeshow.2000.AppliedLogisticRegresion.New York: John Wiley&Sons. Karlson,Kristian B.,Anders Holm,and Richard Breen Comparing Regresion CoefficientsBetweenSame-sample Nested Models UsingLogitandProbit:A New Method. Sociological Methodology42(1): Kohler,Ulrich,KristianB.Karlson,andAndersHolm ComparingCoefficientsof NestedNonlinearProbability Models. TheStataJournal11(3): Long, J.Scot.1997.Regresion Modelsfor Categoricaland Limited Dependent Variables. ThousandOaks:SagePublications. Long, J.ScotandJeremyFreese.2001.Regresion ModelsforCategoricalDependentVariables UsingStata.ColegeStation,Texas:StataPres. Mare,RobertD SocialBackgroundandSchoolContinuationDecisions. Journalof theamerican StatisticalAsociation75(370): Mare,Robert D Changeand Stabilityin EducationalStratification. American SociologicalReview46(1): Mood,Carina LogisticRegresion:Why WeCannotDo WhatWeThink WeCan Do,and WhatWeCanDoAboutIt. European SociologicalReview26: Petersen,Trond A CommentonPresentingResultsfrom LogitandProbitModels. American SociologicalReview50(1): Wang, JiaandYu Xie FeelingGoodAbouttheIronRiceBowl:EconomicSectors andhappinesinpost-reform UrbanChina. SocialScienceResearch53: Wiliams,Richard Using Heterogeneous Choice Modelsto Compare Logitand ProbitCoefficientsAcrosGroups. Sociological Methods&Research37(4): Wiliams,Richard Fiting HeterogeneousChoice Models with Oglm. TheStata Journal10(4): Winship, Christopher and Robert D. Mare Regresion Models with Ordinal Variables. American SociologicalReview49(4): Wooldridge, Jeffrey M.2002.Econometric Analysisof Cros Sectionaland Panel Data. Cambridge:MITPres. : 241

father-in-law on his/herelitestatusatainmentin urban China.Theresults indicatethat(1)father-in-law sculturecapitalhasnoefectsonone selitestatus

father-in-law on his/herelitestatusatainmentin urban China.Theresults indicatethat(1)father-in-law sculturecapitalhasnoefectsonone selitestatus 2017 5 CJS 37 : CGSS2006 : ; ; : DOI:10.15992/j.cnki.31-1123/c.2017.05.008 EffectsofSpouse sfamily Backgroundon EliteStatus AtainmentinUrbanChina ZHU Bin Abstract:Theatainmentofelitestatushaslongbeenamajortopicinthestudyof