--> CLOGIT ; Lhs = mode ; Choices = air,train,bus,car ; Rhs = invc,invt,gc,ttme ; Rh2 = one ; Prob = plist ; List ; Describe ; Crosstab ; Effects : ttme[*] ; Show Model $ Tree Structure Specified for the Nested Logit Model Sample proportions are marginal, not conditional. Choices marked with * are excluded for the IIA test. ----------------+----------------+----------------+----------------+------+--- Trunk (prop.)|Limb (prop.)|Branch (prop.)|Choice (prop.)|Weight|IIA ----------------+----------------+----------------+----------------+------+--- Trunk{1} 1.00000|Lmb[1:1] 1.00000|B(1:1,1) 1.00000|AIR .27619| 1.000| | | |TRAIN .30000| 1.000| | | |BUS .14286| 1.000| | | |CAR .28095| 1.000| ----------------+----------------+----------------+----------------+------+--- Model Specification: Utility Functions for Alternatives Table entry is the attribute that multiplies the indicated parameter. Parameter Row 1 INVC INVT GC TTME A_AIR A_TRAIN A_BUS Choice AIR 1 INVC INVT GC TTME Constant TRAIN 1 INVC INVT GC TTME Constant BUS 1 INVC INVT GC TTME Constant CAR 1 INVC INVT GC TTME Normal exit from iterations. Exit status=0. +---------------------------------------------+ | Discrete choice (multinomial logit) model | | Maximum Likelihood Estimates | | Model estimated: Apr 17, 2006 at 00:10:45PM.| | Dependent variable Choice | | Weighting variable None | | Number of observations 210 | | Iterations completed 6 | | Log likelihood function -184.5067 | | R2=1-LogL/LogL* Log-L fncn R-sqrd RsqAdj | | No coefficients -291.1218 .36622 .35910 | | Constants only -283.7588 .34978 .34247 | | Chi-squared[ 4] = 198.50415 | | Prob [ chi squared > value ] = .00000 | | Response data are given as ind. choice. | | Number of obs.= 210, skipped 0 bad obs. | +---------------------------------------------+ +---------+--------------+----------------+--------+---------+ |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | +---------+--------------+----------------+--------+---------+ INVC -.08493182 .01938251 -4.382 .0000 INVT -.01333220 .00251698 -5.297 .0000 GC .06929537 .01743306 3.975 .0001 TTME -.10364955 .01093815 -9.476 .0000 A_AIR 5.20474275 .90521312 5.750 .0000 A_TRAIN 4.36060457 .51066543 8.539 .0000 A_BUS 3.76323447 .50625946 7.433 .0000 +-------------------------------------------------------------------------+ | Descriptive Statistics for Alternative AIR : | Utility Function | | 58.0 observs. | | Coefficient | All 210.0 obs.|that chose AIR | | Name Value Variable | Mean Std. Dev.|Mean Std. Dev. | | ------------------- -------- | -------------------+------------------- | | INVC -.0849 INVC | 85.252 27.409| 97.569 31.733 | | INVT -.0133 INVT | 133.710 48.521| 124.828 50.288 | | GC .0693 GC | 102.648 30.575| 113.552 33.198 | | TTME -.1036 TTME | 61.010 15.719| 46.534 24.389 | | A_AIR 5.2047 ONE | 1.000 .000| 1.000 .000 | +-------------------------------------------------------------------------+ +-------------------------------------------------------------------------+ | Descriptive Statistics for Alternative TRAIN : | Utility Function | | 63.0 observs. | | Coefficient | All 210.0 obs.|that chose TRAIN | | Name Value Variable | Mean Std. Dev.|Mean Std. Dev. | | ------------------- -------- | -------------------+------------------- | | INVC -.0849 INVC | 51.338 27.032| 37.460 20.676 | | INVT -.0133 INVT | 608.286 251.797| 532.667 249.360 | | GC .0693 GC | 130.200 58.235| 106.619 49.601 | | TTME -.1036 TTME | 35.690 12.279| 28.524 19.354 | | A_TRAIN 4.3606 ONE | 1.000 .000| 1.000 .000 | +-------------------------------------------------------------------------+ +-------------------------------------------------------------------------+ | Descriptive Statistics for Alternative BUS : | Utility Function | | 30.0 observs. | | Coefficient | All 210.0 obs.|that chose BUS | | Name Value Variable | Mean Std. Dev.|Mean Std. Dev. | | ------------------- -------- | -------------------+------------------- | | INVC -.0849 INVC | 33.457 12.591| 33.733 11.023 | | INVT -.0133 INVT | 629.462 235.408| 618.833 273.610 | | GC .0693 GC | 115.257 44.934| 108.133 43.244 | | TTME -.1036 TTME | 41.657 12.077| 25.200 14.919 | | A_BUS 3.7632 ONE | 1.000 .000| 1.000 .000 | +-------------------------------------------------------------------------+ +-------------------------------------------------------------------------+ | Descriptive Statistics for Alternative CAR : | Utility Function | | 59.0 observs. | | Coefficient | All 210.0 obs.|that chose CAR | | Name Value Variable | Mean Std. Dev.|Mean Std. Dev. | | ------------------- -------- | -------------------+------------------- | | INVC -.0849 INVC | 20.995 14.678| 15.644 9.629 | | INVT -.0133 INVT | 573.205 274.855| 527.373 301.131 | | GC .0693 GC | 95.414 46.827| 89.085 49.833 | | TTME -.1036 TTME | .000 .000| .000 .000 | +-------------------------------------------------------------------------+ +------------------------------------------------------+ | Cross tabulation of actual vs. predicted choices. | | Row indicator is actual, column is predicted. | | Predicted total is F(k,j,i)=Sum(i=1,...,N) P(k,j,i). | | Column totals may be subject to rounding error. | +------------------------------------------------------+ Matrix Crosstab has 5 rows and 5 columns. AIR TRAIN BUS CAR Total +---------------------------------------------------------------------- AIR | 34.00000 8.00000 4.00000 13.00000 58.00000 TRAIN | 8.00000 39.00000 4.00000 12.00000 63.00000 BUS | 5.00000 4.00000 17.00000 4.00000 30.00000 CAR | 11.00000 13.00000 5.00000 30.00000 59.00000 Total | 58.00000 63.00000 30.00000 59.00000 210.00000 PREDICTED PROBABILITIES (* marks actual, + marks prediction.) Indiv AIR TRAIN BUS CAR 1 .0563 .2801 .1185 .5451*+ 2 .1097 .2486 .0527 .5889*+ 3 .4181 + .1006 .1075 .3738* 4 .1038 .2209 .0461 .6291*+ 5 .1525 .3760 .0797 .3918*+ 6 .0816 .3013* .2071 .4100 + 7 .9119*+ .0175 .0187 .0519 8 .3738 + .2633 .1437 .2192* 9 .0656 .3265 .1381 .4699*+ 10 .0690 .3097 .1310 .4902*+ 11 .0891 .2628 .0496 .5985*+ 12 .0964 .2315 .0491 .6231*+ 13 .1163 .2439 .0509 .5889*+ 14 .1151 .2764 .0586 .5499*+ 15 .4497 + .2068 .0638 .2798* 16 .0186 .8588*+ .0449 .0776 17 .0151 .8972*+ .0331 .0546 18 .0196 .8441*+ .0580 .0783 19 .0978 .3847*+ .2572 .2603 20 .0087 .9434*+ .0055 .0423 21 .0248 .8221*+ .0632 .0899 22 .1398 .2960* .0659 .4983 + PREDICTED PROBABILITIES (* marks actual, + marks prediction.) Indiv AIR TRAIN BUS CAR 23 .0134* .3520 + .3248 .3098 24 .5461*+ .1627 .1501 .1410 25 .9354*+ .0319 .0120 .0207 26 .9711*+ .0101 .0047 .0141 27 .1162* .3102 + .2862 .2873 28 .5745*+ .1240 .0310 .2705 29 .0927 .0640* .1041 .7392 + 30 .0030 .9742*+ .0077 .0150 31 .0047 .9642*+ .0097 .0214 32 .0173 .8734*+ .0407 .0686 33 .1116 .2998* .0564 .5321 + 34 .0118 .9251*+ .0253 .0379 35 .0131 .8749*+ .0436 .0684 36 .0093 .9290*+ .0210 .0407 37 .1027 .3563* .0568 .4842 + 38 .0587 .6573*+ .0295 .2546 39 .1377 .1270* .0741 .6612 + 40 .9285*+ .0193 .0191 .0330 41 .0738* .3172 + .2927 .3164 42 .6952*+ .1031 .0951 .1066 43 .9099*+ .0310 .0286 .0305 44 .6671*+ .0733 .0295 .2301 PREDICTED PROBABILITIES (* marks actual, + marks prediction.) Indiv AIR TRAIN BUS CAR 45 .4597*+ .1691 .0394 .3319 46 .9693*+ .0102 .0101 .0103 47 .2152* .1755 .0707 .5386 + 48 .6529*+ .1581 .0668 .1221 49 .2887* .2499 .0506 .4109 + 50 .1778* .2242 .2217 .3763 + 51 .0223* .2154 .0867 .6756 + 52 .0176* .2072 .0675 .7077 + 53 .0166 .8719*+ .0379 .0737 54 .0535 .6802*+ .0253 .2411 55 .0168 .9064*+ .0084 .0685 56 .3301 .4632*+ .1131 .0936 57 .4595 + .2337* .1675 .1393 58 .0186 .9301*+ .0049 .0464 59 .4588 + .2387* .1476 .1548 60 .3131 .1092* .0597 .5179 + 61 .5102 + .2030* .1651 .1218 62 .0356 .8399*+ .0164 .1080 63 .0807 .7417*+ .0162 .1614 64 .0374 .9359*+ .0144 .0123 65 .2522 .0121* .0746 .6610 + 66 .1145 .0239 .8395*+ .0220 PREDICTED PROBABILITIES (* marks actual, + marks prediction.) Indiv AIR TRAIN BUS CAR 67 .2880 .0976 .0425 .5719*+ 68 .5562 + .1752 .0930* .1756 69 .2472 .2762* .0437 .4329 + 70 .2017 .2311* .0571 .5101 + 71 .0699 .7736*+ .0157 .1408 72 .2709 .5801*+ .0716 .0775 73 .1614 .7699*+ .0270 .0417 74 .5601 + .0115* .2711 .1572 75 .1228 .5048*+ .0339 .3385 76 .3555 .1426* .0800 .4220 + 77 .4233 + .3093* .1444 .1230 78 .1729 .1814 .0403 .6054*+ 79 .5096 + .2607 .0756 .1541* 80 .3720 .1122 .3859*+ .1299 81 .5594 + .2050 .0085* .2271 82 .1015 .2287 .0538 .6160*+ 83 .0032 .9770*+ .0083 .0115 84 .0552 .6025*+ .1205 .2219 85 .9333*+ .0154 .0062 .0451 86 .0115 .9256*+ .0233 .0395 87 .0847 .2903 .0618 .5632*+ 88 .0097 .9384*+ .0200 .0319 PREDICTED PROBABILITIES (* marks actual, + marks prediction.) Indiv AIR TRAIN BUS CAR 89 .0952 .2580 .0576 .5892*+ 90 .0247 .8446*+ .0130 .1177 91 .0286 .8351*+ .0160 .1203 92 .0104 .9271*+ .0242 .0383 93 .1128 .1209 .0487 .7176*+ 94 .5149*+ .1577 .0334 .2940 95 .7057*+ .0541 .0235 .2167 96 .9467*+ .0160 .0148 .0225 97 .0076 .0509 .9075*+ .0340 98 .8528*+ .0407 .0435 .0631 99 .2355 .1351 .1551* .4743 + 100 .2357 .1202 .0420 .6020*+ 101 .0286 .1561 .7285*+ .0869 102 .2706 .1307 .0379 .5609*+ 103 .0663 .4392 + .1772 .3172* 104 .2736 .1605 .0749 .4910*+ 105 .4364 + .2415 .1127 .2094* 106 .3657 .0734 .4554*+ .1054 107 .3850 + .1248 .1334 .3568* 108 .3117 .1537 .0474 .4871*+ 109 .0949 .2341 .0496 .6213*+ 110 .2502 .1133 .0350 .6015*+ PREDICTED PROBABILITIES (* marks actual, + marks prediction.) Indiv AIR TRAIN BUS CAR 111 .0618 .3329 .1408 .4645*+ 112 .1836 .1029 .0448 .6687*+ 113 .0812* .2848 .0604 .5737 + 114 .8581*+ .0399 .0085 .0936 115 .2338* .2649 .1120 .3893 + 116 .6123*+ .1798 .0761 .1318 117 .0882 .3683 + .2697* .2738 118 .1960 .1069 .6042*+ .0929 119 .0776* .2535 .2710 .3979 + 120 .9744*+ .0123 .0052 .0082 121 .8199*+ .0641 .0130 .1031 122 .0260* .2456 .2626 .4659 + 123 .9886*+ .0039 .0041 .0034 124 .8841*+ .0353 .0084 .0722 125 .0869 .0164 .8701*+ .0265 126 .1296 .0684 .5537*+ .2483 127 .3073 .1192 .0447 .5289*+ 128 .1291 .0726 .5153*+ .2830 129 .0781 .3930 + .1662 .3627* 130 .0122 .9253*+ .0077 .0548 131 .1509 .0805 .0375 .7311*+ 132 .2228 .1087 .0407 .6277*+ PREDICTED PROBABILITIES (* marks actual, + marks prediction.) Indiv AIR TRAIN BUS CAR 133 .2336 .0571 .6275*+ .0819 134 .2252 .1233 .5870*+ .0645 135 .2153 .0923 .0402 .6521*+ 136 .1736 .1274 .0283 .6707*+ 137 .4640 + .1144 .1222 .2994* 138 .1197 .0334 .8163*+ .0307 139 .5915 + .1439 .0834* .1811 140 .2142 .0965 .0362 .6531*+ 141 .3507 .4584*+ .0946 .0963 142 .2950 .4143*+ .1438 .1469 143 .3372 .0012* .0546 .6070 + 144 .0999 .7011*+ .0195 .1796 145 .0689 .8799*+ .0254 .0258 146 .4638 + .1966* .1976 .1420 147 .2574 .5846*+ .0783 .0797 148 .0152 .9524*+ .0033 .0291 149 .0201 .9300*+ .0060 .0439 150 .9050*+ .0296 .0317 .0337 151 .8964*+ .0512 .0279 .0244 152 .7906*+ .0558 .0720 .0816 153 .2030* .1684 .0733 .5553 + 154 .6764*+ .1003 .1072 .1161 PREDICTED PROBABILITIES (* marks actual, + marks prediction.) Indiv AIR TRAIN BUS CAR 155 .2296* .2387 .0506 .4811 + 156 .4188*+ .1843 .0359 .3610 157 .0501* .1732 .0850 .6916 + 158 .9938*+ .0019 .0020 .0023 159 .0073* .3025 .0641 .6261 + 160 .5911*+ .1031 .0215 .2843 161 .1463* .4030 + .1704 .2803 162 .0266* .4419 + .1869 .3446 163 .1530 .1118 .0373 .6979*+ 164 .1867 .1675 .0546 .5912*+ 165 .1627 .1602 .0573 .6198*+ 166 .2889 .2171 .2003 .2937*+ 167 .1787 .1862 .0566 .5785*+ 168 .1633 .1542 .0464 .6361*+ 169 .1983 .1924 .1775 .4317*+ 170 .1816 .1784 .0595 .5804*+ 171 .1472 .1087 .0438 .7003*+ 172 .0928 .4631 + .1134* .3307 173 .0132 .0745 .8573*+ .0550 174 .0336 .0498 .8083*+ .1083 175 .0582 .2745 .1161 .5513*+ 176 .3358 .0834 .4855*+ .0954 PREDICTED PROBABILITIES (* marks actual, + marks prediction.) Indiv AIR TRAIN BUS CAR 177 .0213 .1219 .7663*+ .0905 178 .0154 .0791 .8431*+ .0624 179 .0241* .2391 .0963 .6405 + 180 .9241*+ .0240 .0051 .0469 181 .0948 .3647 .1542 .3864*+ 182 .0682 .3726 .1576 .4016*+ 183 .0422 .7411*+ .0205 .1962 184 .0946 .1292* .0882 .6879 + 185 .0481 .6936*+ .0253 .2330 186 .0473 .0502 .7659*+ .1366 187 .9612*+ .0202 .0076 .0110 188 .9681*+ .0102 .0021 .0196 189 .0637 .3168 .1340 .4855*+ 190 .0692 .3906 + .1996 .3406* 191 .0470 .3039 .1482 .5009*+ 192 .7613*+ .1057 .0447 .0883 193 .9101*+ .0422 .0178 .0299 194 .0613 .1172 .5482*+ .2732 195 .0093 .9507*+ .0044 .0356 196 .0095 .9353*+ .0068 .0484 197 .0692 .4005 + .1580 .3724* 198 .9150*+ .0294 .0271 .0284 PREDICTED PROBABILITIES (* marks actual, + marks prediction.) Indiv AIR TRAIN BUS CAR 199 .9805*+ .0061 .0013 .0121 200 .9827*+ .0055 .0011 .0107 201 .0495 .0400 .7723*+ .1381 202 .2208 .2152 .2128 .3513*+ 203 .0113 .0736 .8758*+ .0394 204 .0161 .0742 .8521*+ .0575 205 .3832 .1087 .3933*+ .1147 206 .2551 .3214 + .2965 .1270* 207 .6175*+ .1365 .1259 .1201 208 .0771 .5140 + .0716* .3373 209 .1698 .3398 + .1944 .2960* 210 .1828 .1762 .0535 .5874*+ +-----------------------------------------------------------+ | Partial effects = average over observations | | | | dlnP[alt=k,br=j,lmb=i,tr=l] | | ---------------------------- = D(m:K,J,I,L) = delta(m)*F | | dx(m):alt=K,br=J,lmb=I,tr=L] | | | | delta(m) = coefficient on x(m) in U(K:J,I,L) | | F = (l=L) (i=I) (j=J) [(k=K)-P(K:JIL)] | | + (l=L) (i=I) [(j=J)-P(J:IL)] P(K:JIL)t(J:IL) | | + (l=L) [(i=I)-P(I:L)] P(J:IL) P(K:JIL)t(J:IL)s(I:L) | | + [(l=L)-P(L)] P(I:L) P(J:IL) P(K:JIL)t(J:IL)s(I:L)f(L) | | | | P(K|JIL)=Prob[choice=K |branch=J,limb=I,trunk=L] | | P(J|IL), P(I³L), P(L) defined likewise. | | (n=N) = 1 if n=N, 0 else, for n=k,j,i,l and N=K,J,I,L. | | Elasticity = x(l) * D(l:K,J,I) | | Marginal effect = P(KJIL)*D = P(K:JIL)P(J:IL)P(I:L)P(L)D | | F is decomposed into the 4 parts in the tables. | +-----------------------------------------------------------+ +-----------------------------------------------------------------+ | Derivative (times 100) Averaged over observations. | | Attribute is TTME in choice AIR | | Effects on probabilities of all choices in the model: | | * indicates direct Derivative effect of the attribute. | | Decomposition of Effect Total | | Trunk Limb Branch Choice Effect| | Trunk=Trunk{1} | | Limb=Lmb[1:1] | | Branch=B(1:1,1) | | * Choice=AIR .000 .000 .000 -1.173 -1.173 | | Choice=TRAIN .000 .000 .000 .376 .376 | | Choice=BUS .000 .000 .000 .241 .241 | | Choice=CAR .000 .000 .000 .556 .556 | +-----------------------------------------------------------------+ +-----------------------------------------------------------------+ | Derivative (times 100) Averaged over observations. | | Attribute is TTME in choice TRAIN | | Effects on probabilities of all choices in the model: | | * indicates direct Derivative effect of the attribute. | | Decomposition of Effect Total | | Trunk Limb Branch Choice Effect| | Trunk=Trunk{1} | | Limb=Lmb[1:1] | | Branch=B(1:1,1) | | Choice=AIR .000 .000 .000 .376 .376 | | * Choice=TRAIN .000 .000 .000 -1.321 -1.321 | | Choice=BUS .000 .000 .000 .258 .258 | | Choice=CAR .000 .000 .000 .688 .688 | +-----------------------------------------------------------------+ +-----------------------------------------------------------------+ | Derivative (times 100) Averaged over observations. | | Attribute is TTME in choice BUS | | Effects on probabilities of all choices in the model: | | * indicates direct Derivative effect of the attribute. | | Decomposition of Effect Total | | Trunk Limb Branch Choice Effect| | Trunk=Trunk{1} | | Limb=Lmb[1:1] | | Branch=B(1:1,1) | | Choice=AIR .000 .000 .000 .241 .241 | | Choice=TRAIN .000 .000 .000 .258 .258 | | * Choice=BUS .000 .000 .000 -.811 -.811 | | Choice=CAR .000 .000 .000 .312 .312 | +-----------------------------------------------------------------+ +-----------------------------------------------------------------+ | Derivative (times 100) Averaged over observations. | | Attribute is TTME in choice CAR | | Effects on probabilities of all choices in the model: | | * indicates direct Derivative effect of the attribute. | | Decomposition of Effect Total | | Trunk Limb Branch Choice Effect| | Trunk=Trunk{1} | | Limb=Lmb[1:1] | | Branch=B(1:1,1) | | Choice=AIR .000 .000 .000 .556 .556 | | Choice=TRAIN .000 .000 .000 .688 .688 | | Choice=BUS .000 .000 .000 .312 .312 | | * Choice=CAR .000 .000 .000 -1.555 -1.555 | +-----------------------------------------------------------------+