Inquire if MNL is necessary when estimating NL model

[linlin zhang]

Dear Michael,

I encounter the following situation when runing the nested logit (NL) model with nine choices and with over 1,200,000 sample.

1) When I directly estimate the NL model, the NL model result show that the nested structure I designed works through judging MU (namely MU_1 as below).
2) However, when I first estimate the MNL model, remove insignificant independent variables in the utility function of each Choice based on MNL model result, and then estimate the NL model, the NL model result show that the same nested structure does not work by judging MU (namely MU_2 as below).
Which NL model 1)2) do you think works?

MU_1   8.943783    1.377819     6.491262  8.512058e-11
MU_2   1.261063    0.226150     5.576219  2.458025e-08


Best, Linlin

[Bierlaire Michel]

On 30 Nov 2022, at 12:24, linlin zhang <linlin...@gmail.com> wrote:

Dear Michael,

I encounter the following situation when runing the nested logit (NL) model with nine choices and with over 1,200,000 sample.

1) When I directly estimate the NL model, the NL model result show that the nested structure I designed works through judging MU (namely MU_1 as below).
2) However, when I first estimate the MNL model, remove insignificant independent variables in the utility function of each Choice based on MNL model result,

This is not a good idea to remove variables, especially if you know that the best model is logit. 

and then estimate the NL model, the NL model result show that the same nested structure does not work by judging MU (namely MU_2 as below).

Why do you say “it does not work”? 

Which NL model 1)2) do you think works?

MU_1   8.943783    1.377819     6.491262  8.512058e-11
MU_2   1.261063    0.226150     5.576219  2.458025e-08


Best, Linlin

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[linlin zhang]

Dear Michael,

1. Then my question is--- how to judge if the Nested Structure I designed in NL model works or not? Through which indicators? I am quite confused.

2. If we consider the following two indicator can  a) MU value is larger than 1; b)(MU-1)/Stderr is larger than 1.96 in my case (with over 1,200,000 observations). Then (MU_2-1)/Stderr=(1.261063-1)/0.226150  is less than 1.96. So that's why I said that does not work.

Best, Linlin

[Bierlaire Michel]

On 1 Dec 2022, at 11:52, linlin zhang <linlin...@gmail.com> wrote:

Dear Michael,

1. Then my question is--- how to judge if the Nested Structure I designed in NL model works or not? Through which indicators? I am quite confused.

A likelihood ratio test would do.

2. If we consider the following two indicator can  a) MU value is larger than 1; b)(MU-1)/Stderr is larger than 1.96 in my case (with over 1,200,000 observations). Then (MU_2-1)/Stderr=(1.261063-1)/0.226150  is less than 1.96. So that's why I said that does not work.

It means that the first nest is meaningful, but not necessarily the second one. You may want to constrain MU_2 to 1. 

Best, Linlin

在2022年11月30日星期三 UTC+1 15:24:50<michel.b...@epfl.ch> 写道：

On 30 Nov 2022, at 12:24, linlin zhang <linlin...@gmail.com> wrote:

Dear Michael,

I encounter the following situation when runing the nested logit (NL) model with nine choices and with over 1,200,000 sample.

1) When I directly estimate the NL model, the NL model result show that the nested structure I designed works through judging MU (namely MU_1 as below).
2) However, when I first estimate the MNL model, remove insignificant independent variables in the utility function of each Choice based on MNL model result,

This is not a good idea to remove variables, especially if you know that the best model is logit. 

and then estimate the NL model, the NL model result show that the same nested structure does not work by judging MU (namely MU_2 as below).

Why do you say “it does not work”? 

Which NL model 1)2) do you think works?

MU_1   8.943783    1.377819     6.491262  8.512058e-11
MU_2   1.261063    0.226150     5.576219  2.458025e-08


Best, Linlin

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[linlin zhang]

Dear Michael,

Thank you for your answer.

1. However, I am quite confused why you refer to the likelihood ratio test? I just want to know how to judge if my NL model works or not, if I understand it clearly, whether NL model works or not is only related to the indicators about MU (such as the Value and P Value of MU). Could you re-answer my question? Otherwise, what is the boundary of the likelihood ratio test when it can represent the NL model works?

2. I think you may misunderstand what MU_1 and MU_2 are. MU_1 and MU_2 mentioned in my previous emails are for the same nesed structures but for different NL models 1) 2), instead of representing two nested structures in one NL model. MU_1 is in the 1) NL model with  putting into all independent variables into each utility function of each Choice. MU_2 is for the 2) NL model with puting only significant independent variables (which is derived from MNL model results) into each utility function of each Choice,

Many thanks.