[Limdep Nlogit List] Problem with Inclusive Value parameterinNested Logit Model.

Mon Apr 13 13:49:38 EST 2009

Dear Duggal,
Again, thank you very much for your consideration and beautiful suggestion on our model. I am trying specifying the model in such the way that you proposed. However, there are things that I did not clearly understand. 
1. The response variable has form of individual data (i.e. it recieves the value of 1 if the corresponding bundle is chosen and 0 otherwise). Moreover, the population proportions are unknown. In such the case, how could we weight the model by using NLOGIT? (What is the variable should be used for the command ;Wts=?)
2. Estimate a degenerate model: you proposed a model with all of the braches are degeneracy. In this case, Neted Logit model collapses to MNL model and we do not have scale parameter for any of the braches any more (all of the IV parameters will receive the value of 1.0 due to degeneracy if RU2 is used. In the cases of RU1 or NNNL, NLOGIT could not estimate the model since the starting value is also the solution). Below is the Note of NLOGIT:

''NOTE: Convergence in initial iterations is rarely
at a true function optimum. This may not be a
solution (especially if initial iterations stopped).
Exit from iterative procedure.    1 iterations completed.
Check convergence values shown below.
Gradient value: Tolerance= .1000D-04, current value= .5647D-09
Function chg. : Tolerance= .0000D+00, current value= .2545D+05
Parameters chg: Tolerance= .0000D+00, current value= .4961D-08
Smallest abs. param. change from start value = .0000D+00
At least one parameter did not leave start value.
Normal exit from iterations. Exit status=0.''

Thus, how can we aggregate bundle choices into a more "appropriate" nested structure based on how close the scale parameters are for each of the 8 alternatives?
3. The model with IV parameter of NOCAR branch constrained to be equal to 1.0 works well with acceptable IV parameter for CAR branch. I am now finding effects of the constraint on coefficient estimates as well as standart errors.

Best regards,
HO, Quoc Chinh.

Nagoya University, school of engineering
Faculty of Civil Engineering.

Email:   hoqchinh at yahoo.com.vn
            chinh at trans.civil.nagoya-u.ac.jp

--- Thứ 2, 13/04/09, Mausam Duggal <DuggalM at mmm.ca> đã viết:

Từ: Mausam Duggal <DuggalM at mmm.ca>
Chủ đề: Re: [Limdep Nlogit List] Problem with Inclusive Value parameterinNested Logit Model.
Đến: "Limdep and Nlogit Mailing List" <limdep at limdep.itls.usyd.edu.au>
Ngày: Thứ Hai, 13 tháng 4, 2009, 0:37

Hi Ho,

Some thoughts on what you could try. 

1.    First, you can weight the model, if you are not already doing so.
2.    Estimate a degenerate model (8 trees with only one elemental alternative in each tree). This will help point towards a more "appropriate" nested structure based on how close the scale parameters are for each of the 8 alternatives.
3.    You also need to constrain the IV parameter to 1.0 for one of the nests. You can try doing that for the non-car mode. ;ivset:(nocar)=[1.0]
4.    Finally, you might want to introduce some of the socio-economic variables in the upper level nest (i.e. in the car or non-car level) while keeping the alternative specific variables in the elemental level (bundel0, bundel1...etc), if things yet don't work.

Thanks.

Mausam Duggal, MCIP, RPP

Senior Project Coordinator

MMM GROUP

100 Commerce Valley Drive West

Thornhill, ON Canada L3T 0A1

T: 905-882-4211, x6289

F: 905-882-7277

W: www.mmm.ca

-----Original Message-----
From: limdep-bounces at limdep.itls.usyd.edu.au [mailto:limdep-bounces at limdep.itls.usyd.edu.au] On Behalf Of ho quoc Chinh
Sent: Sunday, April 12, 2009 12:35 PM
To: Limdep and Nlogit Mailing List
Subject: Re: [Limdep Nlogit List] Problem with Inclusive Value parameterinNested Logit Model.

Dear Duggal,
Thank you for your suggestion. I tried to specify normalization at RU1 with the same starting value and obtained the IV parameters for Car and Nocar branches as 0.445036 and 1.48408, respectively. Both of these parameters are statistically significant at 99% confident level. However, the exit code of NLOGIT is 1 instead of 0. That means the estimation did not really converge. 
Using this result as starting value for another procedure (Adding Maxit =150 to syntax), the exit status is 3 (Error:   806: Line search does not improve fn. Exit iterations. Status=3) at iteration 110. The LLFs at entry and exit are -25517 and -25415, respectively. 
One of the possible reasons for the unconvergence that I guess is the unbalance in sample size of bundles in response variable. Sample size for each bundle is as follows:
Bundle0: 363
Bundel1: 1344
Bundel2: 13170
Bundle3: 10
Bundle4: 12406
Bundle5: 14
Bundle6: 281
Bundle7: 161.
In short, the bundles containing vehicle type Car are small in sample sizes. Any suggestion to overcome such kind of the problem?
Sincerely yours,

HO, Quoc Chinh.
Nagoya University, school of engineering
Faculty of Civil Engineering.

Email:   hoqchinh at yahoo.com.vn
            chinh at trans.civil.nagoya-u.ac.jp

--- Chủ nhật, 12/04/09, Mausam Duggal <DuggalM at mmm.ca> đã viết:

Từ: Mausam Duggal <DuggalM at mmm.ca>
Chủ đề: Re: [Limdep Nlogit List] Problem with Inclusive Value parameter inNested Logit Model.
Đến: "Limdep and Nlogit Mailing List" <limdep at limdep.itls.usyd.edu.au>
Ngày: Chủ nhật, 12 tháng 4, 2009, 22:04

Ho,

For starters, what happens if you specify normalization at RU1 instead of RU2. Ru1 is anyways preferred based on Hensher, Rose and Greene, Applied Choice Analysis, A Primer.

Thanks.

Mausam Duggal, MCIP, RPP

Senior Project Coordinator

MMM GROUP

100 Commerce Valley Drive West

Thornhill, ON Canada L3T 0A1

T: 905-882-4211, x6289

F: 905-882-7277

W: www.mmm.ca

-----Original Message-----
From: limdep-bounces at limdep.itls.usyd.edu.au [mailto:limdep-bounces at limdep.itls.usyd.edu.au] On Behalf Of ho quoc Chinh
Sent: Sunday, April 12, 2009 2:05 AM
To: limdep at limdep.itls.usyd.edu.au
Subject: [Limdep Nlogit List] Problem with Inclusive Value parameter inNested Logit Model.

Dear all,

I am fitting the Nested logit model with NLOGIT version 3.0.
As a response variable we have eight (08) alternatives. They are: 

None(bundle0), Bike only (bundle1), Motorcycle only
(bundle2), car only (bundle3), Bike and Motorcycle (bundle4), Bike and Car
(bundle5), Motorcycle and Car (bundle6) and All of these three vehicles (bundle7).
All attribute parameters are set to be alternative-specific.

The syntax of the model, which I use, is: 

NLOGIT;
Lhs= BUNDLE;

Choices=bundle0,
bundle1, bundle2, bundle3,bundle4, bundle5, bundle6, bundle7;

    Tree= Car(bundle3, bundle5, bundle6,
bundle7),

    NOcar(bundle0,
bundle1,bundle2,bundle4);

    Model: U(bundle0)=0/

    U(bundle1)=
b2*WORKER+b3*NONWORK+b4*CHILD+b6*INC+b8*PPDENS+b9*DIST/

    U(bundle2)=
b10+b11*WORKER+b12*NONWORK+b13*CHILD+b14*HOUSEOWN

                        +b15*INC
+b17*PPDENS +a2*HEADPRO/

    U(bundle4)=
b28+b29*WORKER+b30*NONWORK+b31*CHILD+b32*HOUSEOWN

                        +b33*INC+b34*MIXLAND+b35*PPDENS
+a4*HEADPRO/

    U(bundle3)= b20*HEADPRO/  

    U(bundle5)= b38+b42*INC +b44*PPDENS /

    U(bundle6)=b46+b50*HOUSEOWN+b51*INC+b53*PPDENS+b54*DIST+a6*HEADPRO/

    U(bundle7)=b55+b59*HOUSEOWN+b60*INC+b62*PPDENS
+a7*HEADPRO;

RU2;  

Tlg=0.00001       

$

And
after execution of the model, I obtain the estimates with NEGATIVE Inclusive Value
parameter for Car branch, which can been seen as follow: 

IV parameters, RU2 form =
mu(j|i),gamma(i)

CAR        
-1.881354099       .11426681  -16.465  
.0000

NOCAR       
8.594011416       1.1771514    7.301  
.0000

What does seem to be the problem? And how should we
understand the negative IV parameter since negative sign of IV parameter is in
fact contrary to the literature. 

Moreover, if we let NLOGIT do the above syntax by itself,
convergence cannot be obtained due to LLF improvement problem. Thus, I have
already employed sequential estimation to obtain the starting value for the
above Nested logit model. 

Any sharing of experience, references or hints are highly
appreciated.

Best regards,

HO, Quoc Chinh.

Nagoya
University, school of
engineering

Faculty of Civil Engineering.

Email: hoqchinh at yahoo.com.vn

            chinh at trans.civil.nagoya-u.ac.jp

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