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Question about the specification of the MMNL_inter_intra example

Ask questions about model specifications. Ideally include a mathematical explanation of your proposed model.
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Shawn E
Posts: 1
Joined: 16 Jan 2024, 13:51

Question about the specification of the MMNL_inter_intra example

Post by Shawn E »

Dear Professors,

I am currently working on a model incorporating a random alternative-specific constant to account for inter-intra heterogeneity. In reading your example, I came across the following definition for the random parameter:
randcoeff[["v_tt"]] = ( exp( mu_log_v_tt
+ sigma_log_v_tt_inter * draws_tt_inter
+ sigma_log_v_tt_inter_2 * draws_tt_inter ^ 2
+ sigma_log_v_tt_intra * draws_tt_intra )
* ( gamma_vtt_business * business + ( 1 - business ) ) )
I am seeking clarification on why there is a term "sigma_log_v_tt_inter_2 * draws_tt_inter ^ 2." Additionally, if I intend to create a random constant under a normal distribution, would the following definition be appropriate? :
randcoeff[["asc_none"]] = mu_none + sigma_none * draw_inter + sigma_none_2 * draw_inter^2 + sigma_none_intra * draw_intra

Thanks in advance for your valuable answer.

Best Regards,
Shawn
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dpalma
Posts: 190
Joined: 24 Apr 2020, 17:54

Re: Question about the specification of the MMNL_inter_intra example

Post by dpalma »

Hi Shawn,

It seems to me you are mixing two different things together. The first is the use of polynomial terms in the random components (which is explained in the manual), and the second, and unrelated aspect, is the use of both inter and intra draws. At least as a first step, I would advice against mixing both together. If you are interested in using both inter and intra draws, please do it as below:

Code: Select all

randcoeff[["v_hw"]] =  exp( mu_log_v_hw
                              + sigma_log_v_hw_inter      * draws_hw_inter
                              + sigma_log_v_hw_v_tt_inter * draws_tt_inter )
This is explained in eq. 6.13 in the manual.

Best
David
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