Hello and a question about a parameter inside a log.

[John Abraham]

Greetings friends.  I'm happy to be hands-on with estimation again.  I've been on-and-off through the years.  Decades ago I even wrote my own logit estimation software package,  about the same time as the first edition of Biogeme came out, to do the estimation for my M.Sc.  Fun times.  

For many years I've been mostly doing land use modelling, where we tend to do more "calibration" (specifically adjusting constants and dispersion parameters) to match aggregate data, and a lot less "estimation", partly because we take a more Bayesian approach where a lot of the sensitivity parameters are hard money parameters, that we take from global publications and experience, since local data doesn't have enough variation to estimate them.  For example, it's hard to estimate the nuanced costs and benefits of constructing a hospital from discrete observations of hospital construction when perhaps only one or two hospitals have been constructed in the region for a decade. 

Not that we haven't done some great estimations lately, but I personally haven't been too hands-on with them.

Although I mostly just wanted to introduce myself and say hi to old and new friends, I do have a question that prompted me to write:

I'm trying a modified size term in a multinomial logit

Beta1 * log (size + Beta2) 

and Biogeme is having trouble with Beta2 even with a lower bound of 1.0 on it. It spends a lot of time estimating, I keep throwing bigger computers at it, and it still stops after 1000 iterations and 18 hours without converging.  Has anyone estimated a model of this form?  I know it's not a very standard form. If it fails to converge again, I suppose I can inspect the gradient to see what's up?  Perhaps the gradient is just too flat on this parameter.  Right now I'm trying it with Beta1 fixed at 1.0, just to see. 

(I'm trying this because size isn't a true measure of the opportunities available, so I want to dilute its influence a little, especially if the size is quite small, but I still would like  Beta1 to be close to 1.0).

Thanks everyone. 

—

John Abraham

HBA Specto Incorporated

j...@hbaspecto.com

+1-403-232-1060 x1

[John Abraham]

Update regarding the estimation, I fixed Beta1 to 1.0 to try it.   21 hours on a 32core/64thread machine, 100 iterations, didn't converge.  The Beta2 parameter has a really high stderr, value is 155 stderr is 1.8e+308.  Maybe this isn't a good functional form.

[Michel Bierlaire]

Hi John,

> On 1 Apr 2025, at 23:06, John Abraham <j...@hbaspecto.com> wrote:
>
> Greetings friends. I'm happy to be hands-on with estimation again. I've been on-and-off through the years. Decades ago I even wrote my own logit estimation software package, about the same time as the first edition of Biogeme came out, to do the estimation for my M.Sc. Fun times.
>
> For many years I've been mostly doing land use modelling, where we tend to do more "calibration" (specifically adjusting constants and dispersion parameters) to match aggregate data, and a lot less "estimation", partly because we take a more Bayesian approach where a lot of the sensitivity parameters are hard money parameters, that we take from global publications and experience, since local data doesn't have enough variation to estimate them. For example, it's hard to estimate the nuanced costs and benefits of constructing a hospital from discrete observations of hospital construction when perhaps only one or two hospitals have been constructed in the region for a decade.
>
> Not that we haven't done some great estimations lately, but I personally haven't been too hands-on with them.
>
> Although I mostly just wanted to introduce myself and say hi to old and new friends, I do have a question that prompted me to write:
>
> I'm trying a modified size term in a multinomial logit
>
> Beta1 * log (size + Beta2)
>
> and Biogeme is having trouble with Beta2 even with a lower bound of 1.0 on it. It spends a lot of time estimating, I keep throwing bigger computers at it, and it still stops after 1000 iterations and 18 hours without converging.

It's a sign that there is a specification issue. Did you try a simple logit first? Are the parameters estimated with high precision? If not, you may want to strengthen the simple model first, before moving to a fancier one.

> Has anyone estimated a model of this form? I know it's not a very standard form. If it fails to converge again, I suppose I can inspect the gradient to see what's up? Perhaps the gradient is just too flat on this parameter. Right now I'm trying it with Beta1 fixed at 1.0, just to see.
>
> (I'm trying this because size isn't a true measure of the opportunities available, so I want to dilute its influence a little, especially if the size is quite small, but I still would like Beta1 to be close to 1.0).
>
> Thanks everyone.
>
> —
> John Abraham
> HBA Specto Incorporated
> j...@hbaspecto.com
> +1-403-232-1060 x1
>
>
>
>

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