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Latent class model WTP and post-estimation

Ask questions about post-estimation functions (e.g. prediction, conditionals, etc) or other processing of results.
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DavidKL
Posts: 14
Joined: 27 Mar 2021, 16:30

Latent class model WTP and post-estimation

Post by DavidKL » 28 Apr 2021, 17:32

Hi David and Stephane!

I have two question for you.

1. How can I explain that, when I get extremely large WTP value for a certain attribute in case of latent class model (in one class).

For example: I have price attribute with 1$, 1.5$, 2$, 2.5$ levels for my analysed product/service and in one class, I get 3$ WTP for a certain attribute level.

How can I explain these? Have any suggestion in literature for this topic?


2. The post analysis in latent class model, you show that (in example on website) how can we distinguish respondents according different variables (for example commute, car availability), what are the frequencies of certain respondents in each class.
If I understand correctly, then in this case I can use Chi^2 test in order to test the existence of difference between groups.
But what can I use, when I want to analyse differences between groups in terms of scale type variables, for example age in year? How can I use for example independent sample t-test, Mann Whitney or Kruskal Wallis test in this case?


Thank you very much for your answer!

Best regards,
David

stephanehess
Site Admin
Posts: 558
Joined: 24 Apr 2020, 16:29

Re: Latent class model WTP and post-estimation

Post by stephanehess » 12 May 2021, 16:04

David

on point 1, this happens a lot with latent class, if the denominator for your MRS is very close to zero in one class, or not different from zero. The same issues as for Mixed Logit (cf. http://www.stephanehess.me.uk/papers/jo ... n_2012.pdf) arise of course if the parameter goes to zero. One solution would be to work in WTP space.

on point 2, I've never done tests like that, but you should know that the posteriors just give you an expected value for a covariate in each class, and this has a standard deviation around it too

Stephane
--------------------------------
Stephane Hess
www.stephanehess.me.uk

martinf
Posts: 2
Joined: 11 May 2021, 16:20

Re: Latent class model WTP and post-estimation

Post by martinf » 11 Jun 2021, 15:35

Hi,
I am writing to you because I have a question about WTP evaluation.
For the context, I use a DCE to evaluation the price that individuals would be willing to pay for a change in energy mix according to three variables: an increase in wind energy in %, an increase in PV energy in % and an increase in mechanization energy in % (these variables follow a normal distribution in the RPL model) and finally my price variables which is an increase in the price per 100 kWh (inverse log normal distribution in RPL).
My price attributs levels: 0€; 1€; 2€, 4€; 6€.

I run a model in MNL and then RPL to make an evaluation of the WTP. Then, I decided to put the WTP in WTP space because it is recommended to use WTP space in the case of a normal log distribution of my price attribut.
To do this, I first tested the WTP space with the model in MNL (see MNL WTP.txt) and whether it is in preference space or in WTP space, the results are the same. On the other hand, when I switch to a model in RPL, then when I estimate my RPL in preference space (RPL.txt) and in WTP space (WTP.txt), I don't get the same results. We can also see that the RPL model allows a better estimation than the WTP space model (in terms of LL).

So, I ask you this question: the two models ( MNL and RPL) without including the WTP space seem to tend towards the same estimates but the outputs evaluate the WTP in a very important way which gives results that sometimes exceed my base price variable (going to a maximum of 6 €) whereas the model in WTP space gives me more consistent results.

Is it normal to have this kind of difference between my two models?
You suggest in this article (http://www.stephanehess.me.uk/papers/jo ... n_2012.pdf) to go through the WTP space to get a better estimation but should I keep my model in WTP space even if the LL is lower than the model in RPL?

Thank you for your answer.
Best regards,
Martin
Last edited by martinf on 24 Jun 2021, 10:49, edited 1 time in total.

stephanehess
Site Admin
Posts: 558
Joined: 24 Apr 2020, 16:29

Re: Latent class model WTP and post-estimation

Post by stephanehess » 11 Jun 2021, 16:24

Hi

I'm not quite sure why you say that it is recommended to use WTP space when the cost coefficient is lognormal. If your cost-coefficient is lognormal, then the inverse moments exist (as shown in the paper you reference below), and you can calculate WTP from the preference space model.

The fact that your WTP and preference space models do not give the same fit with mixed logit is simply because the distributional assumptions are different. In the preference space model, you are using Normals for the marginal utilities of the non-price attributes, while in the wtp space model, they are products of normals and lognormal. This is well known and is the reason why you get different fit.

Our paper does not per se say that you should use WTP space. It says that WTP space is an appealing option if you cannot guarantee the existence of WTP moments in preference space, but as the paper also shows, when you use a lognormal for cost, then the moments exist, so you are fine

Hope this helps

Stephane
--------------------------------
Stephane Hess
www.stephanehess.me.uk

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