--> Create ; LINC = LOG(INCOME) ; LBD = LOG(BD1) $ --> Namelist ; W = ONE,SEX,AGE,LINC $ --> Calculate; Trun_V = 100000 $ --> Logit ; LHS = R1 ; RHS = W,LBD $ +------------------------------------------------+ | Multinomial logit model | | There are 2 outcomes for LH variable R1 | | These are the OLS start values based on the | | binary variables for each outcome Y(i) = j. | | Coefficients for LHS=0 outcome are set to 0.0 | +------------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ Characteristics in numerator of Prob[Y = 1] Constant .8884974664 .42509163 2.090 .0366 SEX -.1648484967 .68837523E-01 -2.395 .0166 1.5090909 AGE -.2879987587E-01 .23880387E-01 -1.206 .2278 3.8424242 LINC .1599748572 .57003752E-01 2.806 .0050 6.4365323 LBD -.1360394845 .21044653E-01 -6.464 .0000 8.3395322 Normal exit from iterations. Exit status=0. +---------------------------------------------+ | Multinomial Logit Model | | Maximum Likelihood Estimates | | Dependent variable R1 | | Weighting variable ONE | | Number of observations 165 | | Iterations completed 6 | | Log likelihood function -89.45020 | | Restricted log likelihood -112.4680 | | Chi-squared 46.03567 | | Degrees of freedom 4 | | Significance level .0000000 | +---------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ Characteristics in numerator of Prob[Y = 1] Constant 1.879490503 2.2589169 .832 .4054 SEX -.9603003726 .38069786 -2.522 .0117 1.5090909 AGE -.1770261859 .12810315 -1.382 .1670 3.8424242 LINC .9135743073 .33116827 2.759 .0058 6.4365323 LBD -.7272257410 .13522888 -5.378 .0000 8.3395322 Frequencies of actual & predicted outcomes Predicted outcome has maximum probability. Predicted ------ ---------- + ----- Actual 0 1 | Total ------ ---------- + ----- 0 68 27 | 95 1 24 46 | 70 ------ ---------- + ----- Total 92 73 | 165 --> Namelist ; Z = W,DZERO $ --> Maximize ; Labels = CONS,C_SEX,C_AGE,C_LINC,C_BID ; Start = B ; Maxit = 100 ; Fcn = BVH=LGP(-DOT[Z]-C_BID*LOG(BD2H)) | BVL=LGP(-DOT[Z]-C_BID*LOG(BD2L)) | BVM=LGP(-DOT[Z]-C_BID*LOG(BD1)) | R1*R2*Log(1-BVH) +R1*(1-R2)*Log(BVH-BVM) +(1-R1)*R2*Log(BVM-BVL) +(1-R1)*(1-R2)*Log(BVL) $ Normal exit from iterations. Exit status=0. +---------------------------------------------+ | User Defined Optimization | | Maximum Likelihood Estimates | | Dependent variable Function | | Weighting variable ONE | | Number of observations 165 | | Iterations completed 11 | | Log likelihood function -216.2163 | +---------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ CONS 6.675837357 2.0511996 3.255 .0011 C_SEX -1.011809305 .32109361 -3.151 .0016 C_AGE -.2318059529 .10818015 -2.143 .0321 C_LINC 1.000013397 .29618030 3.376 .0007 C_BID -1.332387780 .12838680 -10.378 .0000 --> Calculate; K = Row(B) ; K1 = K-1 $ --> Matrix; Nobs=NREG ; Cvec=Part(B,1,K1) ; Cbid=Part(B,K,K) ; Xvec=Mean(W) ; Const=Cvec' * Xvec $ --> Calculate; Nab1 = -1/Cbid ; Nab2 = Const/((Cbid)^2) $ --> Matrix; Nab3 = Xvec * Nab1 ; Nab = [Nab3/Nab2] ; AsyVar = Nab' * VARB * Nab $ --> Fintegrate ;fcn = LGP(Const+Cbid*log(x))/Nobs ;labels = x ;start = 1000 ;pts =100 ;limit = 0.001,Trun_V ;vary(x) $ +---------------------------------------------------+ | Function integration: | | Grid is 100 points in [ .001 to 100000.000] | | Value of the integral is 7351.16956 | +---------------------------------------------------+ --> Calculate; List ; A1 = Const ; B1 = Cbid ; Myu_Est = -Const/Cbid ; WTP_Median = exp(-Const/Cbid) ; WTP_Mean = INTEGRAL ; MaxP = 1-LGP(-(Const + Cbid*log(Trun_V))) ; Trun_Mean = (WTP_Mean-Trun_V*MaxP)/(1-MaxP) ; AVar = AsyVar ; CInt95L = Exp(Ntb(0.025, Myu_Est, AsyVar^(0.5))) ; CInt95U = Exp(Ntb(0.975, Myu_Est, AsyVar^(0.5))) ; CInt90L = Exp(Ntb(0.05, Myu_Est, AsyVar^(0.5))) ; CInt90U = Exp(Ntb(0.95, Myu_Est, AsyVar^(0.5))) ; Log_L = Logl ; AIC = -2*(Logl-K) $ A1 = .10694846810725400D+02 B1 = -.13323877797182350D+01 MYU_EST = .80268274548323170D+01 WTP_MEDI= .30620118763412060D+04 WTP_MEAN= .73511695600827320D+04 MAXP = .95196269597025430D-02 TRUN_MEA= .64607104171786820D+04 AVAR = .14673339496077260D-01 CINT95L = .24148924689927670D+04 CINT95U = .38825400514734190D+04 CINT90L = .25088518028123710D+04 CINT90U = .37371345411298230D+04 LOG_L = -.21621625831507730D+03 AIC = .44243251663015460D+03 --> Maximize ; Labels = CONS,C_SEX,C_AGE,C_LINC,C_BID ; Start = B ; Maxit = 100 ; Fcn = BVH=PHI(-DOT[Z]-C_BID*LOG(BD2H)) | BVL=PHI(-DOT[Z]-C_BID*LOG(BD2L)) | BVM=PHI(-DOT[Z]-C_BID*LOG(BD1)) | R1*R2*Log(1-BVH) +R1*(1-R2)*Log(BVH-BVM) +(1-R1)*R2*Log(BVM-BVL) +(1-R1)*(1-R2)*Log(BVL) $ Normal exit from iterations. Exit status=0. +---------------------------------------------+ | User Defined Optimization | | Maximum Likelihood Estimates | | Dependent variable Function | | Weighting variable ONE | | Number of observations 165 | | Iterations completed 10 | | Log likelihood function -215.4430 | +---------------------------------------------+ +---------+--------------+----------------+--------+---------+----------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| +---------+--------------+----------------+--------+---------+----------+ CONS 3.608594510 1.2567898 2.871 .0041 C_SEX -.5222387571 .18580661 -2.811 .0049 C_AGE -.1072326029 .65158972E-01 -1.646 .0998 C_LINC .5859439481 .17571922 3.335 .0009 C_BID -.7639530580 .60421633E-01 -12.644 .0000 --> Matrix; Nobs=NREG ; Cvec=Part(B,1,K1) ; Cbid=Part(B,K,K) ; Xvec=Mean(W) ; Const=Cvec' * Xvec $ --> Calculate; Nab1 = -1/Cbid ; Nab2 = Const/((Cbid)^2) $ --> Matrix; Nab3 = Xvec * Nab1 ; Nab = [Nab3/Nab2] ; AsyVar = Nab' * VARB * Nab $ --> Fintegrate ;fcn = PHI(Const+Cbid*log(x))/Nobs ;labels = x ;start = 1000 ;pts =100 ;limit = 0.001,Trun_V ;vary(x) $ +---------------------------------------------------+ | Function integration: | | Grid is 100 points in [ .001 to 100000.000] | | Value of the integral is 7393.79282 | +---------------------------------------------------+ --> Calculate; List ; A1 = Const ; B1 = Cbid ; Myu_Est = -Const/Cbid ; WTP_Median = exp(-Const/Cbid) ; WTP_Mean = INTEGRAL ; MaxP = 1-PHI(-(Const + Cbid*log(Trun_V))) ; Trun_Mean = (WTP_Mean-Trun_V*MaxP)/(1-MaxP) ; AVar = AsyVar ; CInt95L = Exp(Ntb(0.025, Myu_Est, AsyVar^(0.5))) ; CInt95U = Exp(Ntb(0.975, Myu_Est, AsyVar^(0.5))) ; CInt90L = Exp(Ntb(0.05, Myu_Est, AsyVar^(0.5))) ; CInt90U = Exp(Ntb(0.95, Myu_Est, AsyVar^(0.5))) ; Log_L = Logl ; AIC = -2*(Logl-K) $ A1 = .61799027235023300D+01 B1 = -.76395305798403140D+00 MYU_EST = .80893749411910940D+01 WTP_MEDI= .32596494607145480D+04 WTP_MEAN= .73937928244374270D+04 MAXP = .44557346051427030D-02 TRUN_MEA= .69793173497587500D+04 AVAR = .16240127869253270D-01 CINT95L = .25391977933714780D+04 CINT95U = .41845163202675050D+04 CINT90L = .26432384337824490D+04 CINT90U = .40198093637528890D+04 LOG_L = -.21544304233744110D+03 AIC = .44088608467488210D+03