Using logitr to estimate heterogeneity in customers time-preferences about logitr HOT 4 CLOSED

Hi Moritz, thanks for your kind words! Can you tell me a bit more about how you're specifying the model? Are you estimating a WTP space model? It might help if you pasted in your code so I could see how you're specifying it.

I'm having a difficult time understanding how a WTP space model would work here. For WTP space models, you need a "price" attribute that everything is normalized to. Is the upfrontCost variable the price? If so, then I believe the WTP space model would look like this:

U_i = λ_i (ω1 * futureSavings_i - upfrontCost_i ) + ε_i

This seems a bit strange as ω1 is the WTP for futureSavings. But perhaps that's what you're after? That is, rather than using the words "willingness to pay," you could interpret it as the "value" of those future savings?

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Thank you for your prompt reply!
Here is a commented example of my modelling approach: https://rpubs.com/mwussow/904254

As shown:

• preference and WTP space produce the same parameter estimates (as expected)
• paramter of interest is distributed in the sample (as shown by interaction model)
• mixed logit in both preference and WTP space fail to capture heterogeneity of parameters

My best guess is that it might be related to the fact that the attributes of the alternatives vary over individuals (could this violate a model assumption?)

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This all looks correct to me. The code appears to be correctly implemented. The only potential errors I see are:

• obs_ID starts at 0. This shouldn't matter, but it's probably better to have it start at 1.
• In 4.2 (Mixed-logit, WTP space) you have randPars = c(invest = 'n', invest = 'n'). Should be randPars = c(invest = 'n').

Pretty sure neither matter though.

In terms of why the sigma terms are small in the mixed logit models, that doesn't seem that odd to me. The interaction model you have shows an insignificant interaction effect:

## Model Coefficients: 
##               Estimate Std. Error z-value  Pr(>|z|)    
## invest         11.3238     1.4386  7.8716 3.553e-15 ***
## savings       152.5849    18.7007  8.1593 4.441e-16 ***
## savings_group  33.4926    31.2658  1.0712    0.2841    
## invest_group   -1.1794     2.1722 -0.5429    0.5872    

The standard errors on the interaction terms are huge, so the could just as well be zero, meaning there's no measurable difference between these groups. So it's not surprising to me that the mixed logit models suggest that there is little heterogeneity. The log-likelihood values are all the same too, so it looks like they're all converging to the same solutions.

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Thank you for pointing this out! I am puzzled how I could have missed it.
I think this explains the model results.

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