GONG
Assignment Cheng 3
1. Explore the data
When we use crosstab to analysis the decision, we first draw a graph (Fig 1.1),
which is the percentage of alternatives that people can choose when they made
their decision by different range of income. We notice that the number people can
have train is nearly equal to car, which means that when people making their
travel choice, the train and car shares the same chance to be chosen. The air shares
the least percentage.
Fig. 1.1 the percentage of choice
For those the really number of peoples choice, we can get the Table 1.1.
Table 1.1
1(TRAI
3(BUS 4(CAR
INCOME
2(AIR)
SUM
N)
)
)
18.41
71.64
100.00
5000
8.46% 1.49%
%
%
%
85.00
100.00
15000
4.76% 0.71% 9.52%
%
%
2000087.79
100.00
5.15% 0.76% 6.30%
25000
%
%
2500192.68
100.00
6.10% 0.00% 1.22%
30000
%
%
3000190.18
100.00
3.75% 0.71% 5.36%
35000
%
%
3500191.30
100.00
8.70% 0.00% 0.00%
40000
%
%
4000193.62
100.00
1.89% 0.95% 3.55%
45000
%
%
5000093.44
100.00
2.62% 1.31% 2.62%
55000
%
%
92.90
100.00
70000
3.25% 1.83% 2.03%
%
%
89.15
100.00
SUM
4.09% 1.02% 5.74%
%
%
Fig 1.2 distribution of actual choice of traveller
The distribution of car uses the second y-coordination, which is on the right side. From
Fig 1.2 we can easliy get the distribution of actual choice of traveller. For bus, when the
annual income is 5000, the people are willing to take bus instead of other alternatives.
For train, the distribution is similar with the bus, while it shares less percentage than bus
from 5000 to 20000, and than, the distribuion is really the same. Obviously, the most part
of alternatives is car. It has almost more than 90% alternatives after 25000 annual
income. For air, it increases when income increase.
Moreover, we can focus on the gender relationship with the alternatives.
GENDER 1(TRAI
2(AIR) 3(BUS 4(CAR SUM
Cheng GONG
N)
)
0
2.50%
0.91%
)
3.41% 93.18%
1
6.06%
1.17%
8.61% 84.16%
100.0
0%
100.0
0%
Table 1.2
It is very interesting that for female, they usually choose train, air and bus than male. And
we find that in these 3032 cases, our sample includes 1199 female and 1833 male. So
even the number of male is larger than female, we found that more male will try car than
other alternatives. Maybe it is because the car is more convenience than others, and the
men dont like inconvenience choices. Due to those unrealistic data, in this part we just
ignore them. In the rest part, for these 58 data, so we replace 0 and 1 into 0.6
(1833/3032).
2. Estimate a basic reference model
The travel time (TT) and travel cost (TC) variables are specified as generic in this model.
After running the Elm, we can first get the estimation of a constant only model, which
states in Table 2.1. Notice, we set car as a base.
Table 2.1Constant only Model Estimates
Model
Parameter
Estimates
Parameter
InitValue
FinalValue
StdError
t-Stat
NullValue
cnst_CO@T
rain
0
cnst_CO@
Air
0
cnst_CO@
Bus
0
Log Likelihood at Convergence
-3.0794
0.091844
-33.529
0
-4.0295
0.18114
-22.245
0
-2.3485
0.079287
-29.62
0
-1266.26034
Log Likelihood at Null
-3582.76946
Parameters
The Adjusted Rho Squared with respect to zero is 0.653.
Then we build a basic reference model that includes only the alternative specific
constants, travel time and travel cost. Due to travel time, firstly, we use total travel time.
We can get Table 2.2 for this basic reference model.
Table 2.2 Basic Reference Model Estimates
Parameter
InitValue
FinalValue
StdError
t-Stat
NullValue
cnst_CO@T
rain
0
-2.4536
0.13326
-18.412
0
cnst_CO@A
ir
0
-4.1884
0.66378
-6.3098
0
cnst_CO@B
us
0
-1.5654
0.12976
-12.063
0
COST
0
-0.0058552
0.008924
-0.65613
0
Cheng GONG
Time
0
-0.008364
Log Likelihood at Convergence
Log Likelihood at Null
Parameters
0.001122
-7.4576
0
-1237.05329
-3582.76946
The Adjusted Rho Squared with respect to zero is 0.653. The Adjusted Rho Squared with
respect to constants only is 0.021.
For this basic reference model, we can build a table (Table 2.3) shows the likelihood ratio
test for hypothesis.
Table 2.3 Test for Hypothesis
Variables
Test for Hypothesis Ho,1
Test for Hypothesis Ho,2
Log-Likelihood of Unrestricted
-1266.26034
-1237.05329
Model
Log-Likelihood of restricted
-3582.76946
-1266.26034
Model
Test Statistics (-2(LLr-LLu))
4633.01824
58.4141
Number of Restriction
4
6
Critical Chi-Spqured Value
0
9.44499E-11
It is obvious that for a constant only model is much better than a null parameters model,
meanwhile, the basic reference model is better than constant only model, as from Table
2.3 we reject the hypothesis. (Reject H0 with a level of significance less than 0.05.) Also
it is clear that the reference model has a better goodness.
In my table I use a function in Excel CHISQ.DIST.RT. Or I can find the significance level
0.01 in freedom 6 is 16.812, which is less than 58.4141.
3. Impact of frequency on mode choice
Table 3.1 Estimation on model adding FREQ
Parameter
InitValue
FinalValue
StdError
t-Stat
NullValue
cnst_CO@T
rain
0
-2.8658
0.15574
-18.402
0
cnst_CO@A
ir
0
-5.4139
0.84562
-6.4022
0
cnst_CO@B
us
0
-2.3835
0.20278
-11.754
0
COST
0
-0.0056449
0.011139
-0.50676
0
FREQ
0
0.053116
0.009284
5.7213
0
Time
0
-0.0062771
0.001326
-4.7351
0
Log Likelihood at Convergence
-1219.21608
Log Likelihood at Null
Parameters
Parameter
cnst_CO@T
-3582.76946
Table 3.2 Estimation on model adding FREQ2
InitValue
FinalValue
StdError
t-Stat
NullValue
0
50.197
9.2044
5.4536
0
Cheng GONG
rain
cnst_CO@A
0
47.649
ir
cnst_CO@B
0
50.68
us
COST
0
-0.0056449
FREQ2
0
0.053116
Time
0
-0.0062771
Log Likelihood at Convergence
9.1469
5.2093
0
9.1215
5.5561
0
0.011139
0.009284
0.001326
-0.50676
5.7213
-4.7351
0
0
0
-1219.21608
Log Likelihood at Null
Parameters
-3582.76946
From Table 3.1 and 3.2, except of the constant part, the other parts, which are in grey, are
same. This means that the two models or the probability are the same (Gumble
distribution). The difference part is the constant part as the Car alternative is expressed as
0 in FREQ and as 999 in FREQ2. As car is the base, part will not change, while for
constant part it will change the final number.
4. Explore other models with alternative specific variables
For this part, I will try some model and find the top 2 model for at last.
(1) Add income as a specific variable. Choose the model in Que 2 as the base model,
we call model M1. Then we call the model we will build M2.
Parameter
cnst_CO
@Train
cnst_CO
@Air
cnst_CO
@Bus
INCOME
_CO@Tra
in
INCOME
_CO@Air
INCOME
_CO@Bus
COST
Table 4.1 Estimate the model M2
InitValue
FinalValue StdError
t-Stat
NullValue
0
-1.7165
0.21301
-8.0584
0
Time
Log Likelihood
at Convergence
Log Likelihood
0
-4.474
0.80366
-5.567
0
0
-0.16988
0.19511
-0.87071
0
0
-2.01E-05
5.12E-06
-3.9239
0
0
8.57E-06
9.22E-06
0.93017
0
0
-4.23E-05
5.07E-06
-8.3412
0
0
0.0074076
0.0087339
0.009163
-0.80842
0
0.001137
-7.6829
0
0
-1188.12414
-3582.76946
Cheng GONG
at Null Parameters
Table 4.2 the hypothesis of M1 and M2
Variables
Test for Hypothesis Ho,1
Log-Likelihood of Unrestricted
-1188.12414
Model
Log-Likelihood of restricted
-1237.05329
Model
Test Statistics (-2(LLr-Llu))
97.8583
Number of Restriction
10
Critical Chi-Spqured Value
1.46089E-16
The significance level of 0.01 of freedom 10 is 23.20, which is less than 97.8583. We
can reject the hypothesis. This result means when we add income as a specific
variable it will give a better goodness fit.
(2) Add drive time as a specific variable. Choose the model in Que 2 as the base
model. We call this model M3.
Table 4.3 Estimates of model M3
Parameter
InitValue
FinalValue
StdError
t-Stat
NullValue
cnst_CO@T
0
-3.4832
0.21183
-16.444
0
rain
cnst_CO@A
0
-5.5712
0.72925
-7.6395
0
ir
cnst_CO@B
0
-2.4796
0.2102
-11.796
0
us
DRIVETIM
0
0.0049666
0.00082891
5.9918
0
E_CO@Trai
n
DRIVETIM
0
0.010889
0.0022408
4.8596
0
E_CO@Air
DRIVETIM
0
0.0037253
0.00089441
4.165
0
E_CO@Bus
COST
0
-0.024943
0.0099205
-2.5143
0
Time
0
-0.0038124
0.0013784
-2.7658
0
Log Likelihood
-1202.09949
at Convergence
Log Likelihood
-3582.76946
at Null Parameters
Variables
Test for Hypothesis Ho,1
Log-Likelihood
ofUnrestricted Model
-1202.09949
Log-Likelihood of
-1219.21608
restricted Model
Test Statistics (-2(LLr-Llu))
34.23318
Number of Restriction
10
Cheng GONG
The significance level of 0.01 of freedom 10 is 23.20, which is less than
34.23318.
(3) Add gender as a specific variable. Choose the model in Que 2 as the base model.
We call this model M4.
Table 4.4 Estimates of model M4
Parameter
InitValue
FinalValue
StdError
t-Stat
NullValue
cnst_CO@
0
-2.9835
0.18546
-16.087
0
Train
cnst_CO@
0
-4.3373
0.67453
-6.4302
0
Air
cnst_CO@
0
-2.1442
0.17019
-12.599
0
Bus
GENDER_
0
0.99108
0.19531
5.0744
0
CO@Train
GENDER_
0
0.35567
0.35561
1.0002
0
CO@Air
GENDER_
0
1.0801
0.16987
6.3582
0
CO@Bus
COST
0
-0.006221
0.0087879
-0.7079
0
Time
0
-0.0084651
0.0011251
-7.5239
0
Log Likelihood
-1201.16550
at Convergence
Log Likelihood
-3582.76946
at Null Parameters
Variables
Test for Hypothesis Ho
Log-Likelihood of
Unrestricted Model
-1201.1655
Log-Likelihood of
-1219.21608
restricted Model
Test Statistics (2(LLr-Llu))
36.10116
Number of
Restriction
10
Critical ChiSpqured Value
2.7583E-07
(4) Add income and gender as a specific variable. Choose the model in Que 2 as the
base model. We call this model M5.
Parameter
cnst_CO@
Train
cnst_CO@
InitValue
0
0
Table 4.5 Estimates of model M5
FinalValue StdError
t-Stat
-2.2519
0.24923
-9.0353
-4.6036
0.81067
-5.6788
NullValue
0
0
Cheng GONG
Air
cnst_CO@
Bus
GENDER_
CO@Train
GENDER_
CO@Air
GENDER_
CO@Bus
INCOME_
CO@Train
INCOME_
CO@Air
INCOME_
CO@Bus
COST
Time
Log Likelihood
at Convergence
Log Likelihood
at Null Parameters
0
-0.76074
0.2265
-3.3587
0
0
0.98762
0.19586
5.0425
0
0
0.36827
0.35737
1.0305
0
0
1.0196
0.17302
5.8931
0
0
-1.9757e005
8.6265e006
-4.0618e005
-0.0081969
-0.0088548
5.0855e006
9.1809e006
5.0523e006
0.0090268
0.0011404
-3.8851
0
0.93962
0
-8.0395
0
0
0
0
0
Build a comparison table to M2 and M5:
-0.90806
-7.765
0
0
-1155.72898
-3582.76946
Cheng GONG
Table 4.6 Comparison between M2 and M5
Variables
M2
M5
Travel Cost ($)
-0.0058552 (-0.0081969(-0.91)
0.65613)
Total Travel Time (minutes)
-0.008364 (-0.0088548(-7.765)
0.65613)
Income Variables
Train
-0.0000201(-3.92)
-0.000019757(3.88)
Air
0.00000857(0.93) 0.0000086265(0.94)
Bus
-0.0000423(-8.34)
-0.000040618(8.04)
Car (base)
0
0
Gender Variables
Train
0.98762(5.04)
Air
0.36827(1.03)
Bus
1.0196(5.89)
Car (base)
0
Mode Constants
Train
-1.7165(-8.06)
-2.2519(-9.03)
Air
-4.474(-5.57)
-4.6036(-5.68)
Bus
-0.16988(-0.87)
-0.76074(-3.36)
Car (base)
0
0
Log-likelihood at Zero
-3582.769
-3582.769
Log-likelihood at Constants
-1219.66087
-1188.14388
Log-likelihood at Convergence
-1188.12414
-1155.72898
Ajust-Rho-Squared w.r.t Zero
0.666
0.674
Ajust-Rho-Squared w.r.t Constants
0.022
0.02
Likelihood Ratio Test to Reject
Model M2
Likelihood Ratio
NA
32
Degrees of freedom
NA
1
Rejection Significance
NA
29.141
We can get model M5 is better than model M2, as 32>29.141, so we a find better model
M5.
Even we can get better likelihood like separate travel time into out and in; therefore, we
can get likelihood -1140.65277. I will not continue to do that.
As a conclusion, M5 is a preferred model which has been done above. I think for income
it is for sure must be included. And for gender, as I have done in Que1, the crosstab of
gender, it may be a effective part to include gender.
We cannot easily explain why the data under gender is positive when the base car is
0. Female prefer to get bus more or by car less. Due to this situation, we change our
model in ELM, from (base) car to (base) air. See what we can get:
Cheng GONG
Parameter
cnst_CO@Train
cnst_CO@Car
cnst_CO@Bus
INCOME_CO@Tra
in
INCOME_CO@Car
InitValu
e
0
0
0
0
0
INCOME_CO@Bu
s
GENDER_CO@Tra
in
GENDER_CO@Ca
r
GENDER_CO@Bu
s
D_COST
0
Time
0
Table 4.7
FinalValu StdErro
e
r
2.7774 0.56426
5.0563 0.49671
4.2672 0.56291
-3.09E-05
1.05E05
-1.16E-05
9.25E06
-5.19E-05
1.04E05
0.58456 0.41497
0
-0.39935
0
0.61713
0
-0.049274
0
0.008692
8
t-Stat
4.9221
10.18
7.5806
2.9573
1.2523
4.9667
1.4087
0.3695
NullValu
e
0
0
0
0
0
0
0
1.0808
0.40461 1.5253
0
0.01673
9 2.9437
0.00112
6 7.7172
0
0
0
It is obvious to get that the value of GENDER_CO@Car is a negative number which
means that for female, compared with male, they have less willing to choose car,
which definitely match the finding in Que1.
## For Preferred model: not only from likelihood comparison, but also from the value of
time.
The value of time of M5 is 55.54208 dollar/hour it is a little bit higher. For M2 model the
value of time is 6.31dollar/hour, it so low. So considering this part, we should choose M5
too.
## There is an abundance of empirical evidence that travelers are much more sensitive to
out-of-vehicle time than to in-vehicle time and therefore a minute of out-of-vehicle time
will generate a higher disutility than a minute of in-vehicle-time. I will give a further
explicitly explanation of it later.
5. Explore other models with transformations of variables
(1) Replace COST by COSTINC.
Use the M2 mode replaces COST by COSTINC.
The log likelihood of M2 is -1188.12414, while for COSTINC is -1187.35627. The
model M6 is showed like following:
Cheng GONG
Parameter
cnst_CO@
Train
cnst_CO@
Air
cnst_CO@
Bus
INCOME_
CO@Train
INCOME_
CO@Air
INCOME_
CO@Bus
COSTINC
Time
Table 5.1 Estimates of Model M6 related to COSTINC
InitValue
FinalValue StdError
t-Stat
NullValue
0
-1.8589
0.20743
-8.9617
0
Log Likelihood
at Convergence
Log Likelihood
at Null Parameters
0
-5.685
0.63995
-8.8835
0
0
-0.28311
0.1933
-1.4646
0
0
-1.8606e005
1.9178e005
-4.0762e005
84.14
-0.008785
5
5.156e-006
-3.6086
0
1.1268e005
5.1003e006
53.351
0.0011088
1.702
0
-7.9921
0
1.5771
-7.9233
0
0
0
0
0
0
-1187.35627
-3582.76946
Table 5.2 Hypothesis between M2 and M6
Variables
Test for Hypothesis Ho
Log-Likelihood of Unrestricted
-1187.35627
Model
Log-Likelihood of restricted
-1188.12414
Model
Test Statistics (-2(LLr-Llu))
1.53574
Number of Restriction
10
Critical Chi-Spqured Value
0.998819659
As this question does not have this type of restricted-unrestricted relationship, we use
non-nested hypothesis tests.
Significance Level=
But for this question we cannot reject hypothesis easily. For a freedom of 10 the
significant level of 0.01 is 23.209< 1.53574. From this part we also cannot reject this
hypothesis. So even the likelihood is increased a bit, we cannot take the new model
M6 as a better one.
(2) Add frequency transformed
We create two new models M7 and M8. Use Income and Frequency and In-vehicletime and Out-vehicle-time as M7, and replace FREQ to INVFEQ.
Cheng GONG
Parameter
cnst_CO@
Train
cnst_CO@
Air
cnst_CO@
Bus
INCOME_
CO@Train
INCOME_
CO@Air
INCOME_
CO@Bus
COST
FREQ
OVTT
IVTT
Table 5.3 Estimates of Model M7 of FREQ
InitValue
FinalValue StdError
t-Stat
0
-0.89407
0.31763
-2.8148
NullValue
0
0
-4.0641
1.0205
-3.9826
0
0
0.04653
0.32088
0.14501
0
0
-2.03E-05
5.12E-06
-3.9694
0
0
6.12E-06
9.42E-06
0.65005
0
0
-4.18E-05
5.02E-06
-8.3272
0
0
0
0
0
-0.005902
0.056717
-0.019697
0.0052768
0.012184
0.009517
0.002875
0.001467
-0.48442
5.9595
-6.8499
-3.5972
0
0
0
0
Log Likelihood
at Convergence
Log Likelihood
at constant
Log Likelihood
at Null Parameters
Parameter
cnst_CO@
Train
cnst_CO@
Air
cnst_CO@
Bus
INCOME_
CO@Train
INCOME_
CO@Air
INCOME_
CO@Bus
COST
INVFREQ
OVTT
IVTT
-1155.28636
-1219.66087
-3582.76946
Table 5.4 Estimates of Model M8 of INVFREQ
InitValue
FinalValue StdError
t-Stat
0
-0.36222
0.32254
-1.123
NullValue
0
0
-3.1025
0.87608
-3.5413
0
0
0.93286
0.28762
3.2433
0
5.1314e006
9.2125e006
5.0566e006
0.009949
-3.9993
0
0.85147
0
-8.384
0
-0.34961
0
0.43658
0.0028059
0.00125
-3.1514
-6.9404
-5.7478
0
0
0
0
0
0
0
0
0
0
-2.0522e005
7.8441e006
-4.2395e005
-0.003478
2
-1.3758
-0.019474
-0.007184
Cheng GONG
5
Log Likelihood
at Convergence
Log Likelihood
at constant
Log Likelihood
at Null Parameters
-1168.42585
-1219.66087
-3582.76946
It is very clear that -1155.28636>-1168.42585 and it cannot reject the hypothesis. It
also indicates a diminishing effect of increased frequency.
(3) Examine the impact of group size
I use dummy variable to solve this situation.
We set the group size into 2 parts, one is less or equal to 2, the other is larger than 2.
So due to this formulation, we can get two estimation table, Table5.5 and Table 5.6.
Part 1: Small group:
Table 5.5 Estimates of small group size
Parameter InitValue
FinalValue StdError
t-Stat
NullValue
cnst_CO
0
-1.8617
0.237
-7.8552
0
@Train
cnst_CO
0
-5.2047
0.97129
-5.3586
0
@Air
cnst_CO
0
-0.66383
0.26205
-2.5332
0
@Bus
INCOME
0 -1.93E-05
5.29E-06
-3.6533
0
_CO@Tra
in
INCOME
0
4.77E-06
9.74E-06
0.48917
0
_CO@Air
INCOME
0 -4.31E-05
5.44E-06
-7.922
0
_CO@Bus
COST
0
0.011444
-0.71047
0
0.0081307
FREQ
0
0.046895
0.009596
4.8871
0
Time
0
0.001381
-5.4809
0
0.0075664
Log Likelihood at Convergence
-1034.11578
Log Likelihood at Null Parameters
-2833.23135
Part 2: Large group:
Parameter
cnst_CO@
Train
cnst_CO@
Air
Table 5.6 Estimates of small group size
InitValue
FinalValue StdError
t-Stat
0
-3.831
0.89083
-4.3004
0
-4.7857
3.6754
-1.3021
NullValue
0
0
Cheng GONG
cnst_CO@
0
-3.5025
0.90857
-3.855
Bus
INCOME_
0
-2.5413e2.1563e-1.1786
CO@Train
005
005
INCOME_
0
-2.3702e1.3744e-1.7245
CO@Bus
005
005
COST
0
-0.042685
0.054588
-0.78194
FREQ
0
0.097189
0.035342
2.7499
Time
0
0.002092
0.0051385
0.40713
Log Likelihood at Convergence
-112.92892
Log Likelihood at Null Parameters
-749.53811
The sum of log likelihood of these two parts is -1147.0447.
The original table which is not fixed is showed in Table 5.7.
0
0
0
0
0
0
Cheng GONG
Parameter
cnst_CO@
Train
cnst_CO@
Air
cnst_CO@
Bus
INCOME_
CO@Train
INCOME_
CO@Air
INCOME_
CO@Bus
COST
FREQ
GRPSIZE
Time
Table 5.7 Estimation of no fixed model
InitValue
FinalValue StdError
t-Stat
NullValue
0
-2.4089
0.22067
-10.917
0
0
-4.4911
0.92124
-4.8751
0
0
-1.0534
0.27066
-3.892
0
0
-1.97E-05
4.47E-06
-4.4092
0
0
1.17E-05
9.19E-06
1.2725
0
0
-3.80E-05
6.99E-06
-5.4284
0
0
0
0
0
-3.88E-06
0.011432
-0.00034
0
1.43E-05
0.010596
0.001351
0
1.52E-21
7.06E+13
2.16E-35
0
0.001299
-0.08503
0
0.0001104
9
Log Likelihood at Convergence
-1219.33324
Log Likelihood at Null Parameters
-3582.76946
Compared the log likelihood of the dummy variables
Table 5.8 Hypothesis test between two models
Variables
Test for Hypothesis Ho
Log-Likelihood of Unrestricted
-1147.0447
Model
Log-Likelihood of restricted
-1219.33324
Model
Test Statistics (-2(LLr-Llu))
144.57708
Number of Restriction
12
Critical Chi-Spqured Value
7.11731E-25
Also, the 0.01 significance level under freedom 12 is 26.217, which is much less than
144.577. It means that we have a highly confidence to reject the hypothesis. The segment
model is better than original one.
6. Identify a preferred model
Conclude what we have done in these 5 questions.
We add
income,
separated time into in and out of vehicle time
gender(use air as a base)
to build M9 first for a basic model.
Cheng GONG
Parameter
cnst_CO
@Train
cnst_CO
@Car
cnst_CO
@Bus
INCOME
_CO@Tra
in
INCOME
_CO@Car
INCOME
_CO@Bus
GENDER
_CO@Tra
in
GENDER
_CO@Car
GENDER
_CO@Bus
COST
Table 6.1 Estimate the model M9 (basic model)
InitValue
FinalValue StdError
t-Stat
NullValue
0
2.1217
0.8221
2.5809
0
OVTT
IVTT
Log Likelihood
at Convergence
Log Likelihood
at constant
Log Likelihood
at Null Parameters
0
3.2275
0.87695
3.6804
0
0
3.467
0.83893
4.1326
0
0
-2.82E-05
1.04E-05
-2.7056
0
0
-8.05E-06
9.20E-06
-0.87529
0
0
-4.88E-05
1.04E-05
-4.6988
0
0
0.62513
0.41387
1.5104
0
0
-0.35556
0.36742
-0.96773
0
0
0.67891
0.40292
1.685
0
0
0.0054925
-0.020985
0.0077594
0.009515
-0.57724
0
0.002785
0.001228
-7.5347
-6.3177
0
0
0
0
-1144.31176
-1190.04630
-3582.76946
Transform INCOME to LOGINCOME, add DRIVETIME, add FREQ1 to M10.
Table 6.2 Estimates of Model M10
Parameter
InitValue
FinalValue StdError
t-Stat
NullValue
cnst_CO@
0
6.9762
3.5607
1.9592
0
Train
cnst_CO@
0
3.1796
3.4674
0.917
0
Car
cnst_CO@
0
10.997
3.5274
3.1176
0
Bus
LOGINCO
0
-0.50437
0.31728
-1.5897
0
ME_CO@
Cheng GONG
Train
LOGINCO
ME_CO@
Car
LOGINCO
ME_CO@
Bus
GENDER_
CO@Train
GENDER_
CO@Car
GENDER_
CO@Bus
COSTLNI
NC
OVTT
IVTT
DRIVETI
ME
FREQ
Log Likelihood
at Convergence
Log Likelihood
at constant
Log Likelihood
at Null Parameters
0
0.068616
0.29969
0.22896
0
0
-0.87556
0.31105
-2.8148
0
0
0.67512
0.41661
1.6205
0
0
-0.28896
0.37068
-0.77954
0
0
0.74384
0.40663
1.8293
0
0
-0.061978
0.11873
-0.52199
0
0
0
0
-0.02031
-0.0056146
0.13969
0.002908
0.00147
1.26E+12
-6.9849
-3.8183
1.11E-13
0
0
0
0
0.054966
0.009576
5.74
0
-1122.58621
-1187.40705
-3582.76946
Transform COST into COSTLNINCK, delete GENDER, add LCITY to M11
Table 6.3 Estimates of model M11
Parameter
InitValue
FinalValue
StdError
t-Stat
NullValue
cnst_CO@T
0
8.1766
4.3317
1.8876
rain
cnst_CO@
0
3.8704
4.4856
0.86286
Car
cnst_CO@
0
12.55
4.3455
2.888
Bus
LOGINCO
0
-0.54671
0.38108
-1.4346
ME_CO@T
rain
LOGINCO
0
0.030306
0.38703
0.078303
ME_CO@C
ar
LOGINCO
0
-0.94764
0.37925
-2.4987
ME_CO@B
us
0
0
0
0
0
0
Cheng GONG
COSTLNIN
CK
OVTT
IVTT
DRIVETIM
E
FREQ
LCITY
Log Likelihood
at Convergence
Log Likelihood
at constant
Log Likelihood
at Null Parameters
0
-7.81E-07
0.029545
-2.64E-05
0
0
0
0
-0.020115
-0.0057088
-0.81041
0.002862
0.001432
1.26E+12
-7.0293
-3.9875
-6.42E-13
0
0
0
0
0
0.054387
132.38
0.009381
4.91E+14
5.7975
2.70E-13
0
0
-1151.99741
-1215.94945
-3582.76946
Use Excel to do the non-nested hypothesis:
Table 6.4 Non-nested hypothesis
LL(S)
DoF(S)
RS(S)
LL(I)
1122.58621
1122.58621
17 0.68429831
5
14 0.68471698
6
RS(I)
ST
LoS
0.6799765
77 5.5648522
0.6786530
86 6.5917448
4
DoF(I
)
-1138.07
17
1144.3117
6
14
1.312E-08
2.173E-11
We can have a very high significance to reject the hypothesis. It means that,
compared with the basic model, this one is much better, which I choose it to be the
preferred model.