Hello,
I just wanted to clarify a bit how we present utilities after scaling the values when we do linear coding. I'm trying an HB model where I do purely part-worth values, and another one where I have mostly linear variables, to compare what nuances could be missed if we only do linear variables. I'm presenting this academically, so my end product at this stage is showing the average utilities that come out and I'll be simulating their effects in a later stage (using the raw utilities). For my transportation survey, two of my variables were parking cost and fare:
- Parking cost levels: $0, $3, $7.50, $15
- Fare levels: $0, $2, $3.50, $5
Parking cost was only for auto alternatives, fare was only for transit alternatives. For my linearly coded model, the first time I ran the model I just typed my values in as the level coding:
- Parking cost: 0, 3, 7.5, 15
- Fare: 0, 2, 3.5, 5
I got zero-centred average utilities at the end of -10.75 for parking cost and -8.55 for fare. I realized after that this doesn't follow the coding guidelines for HB (because variance is set to 1, and assumes betas that are mostly in single digits), so I adjusted parking cost and left fare:
- Parking cost: 0, 0.3, 0.75, 1.5
- Fare: 0, 2, 3.5, 5
This time, I got zero-centred average utilities of -120.46 for parking cost and -6.85 for fare. I expected the values to change somewhat, which is fine, but my question is about how to present this afterwards. Fare is clearly on the same order of magnitude and the parking cost is on an order 10x higher, I'd assume this is because my original utilities were both "units per dollar" originally, but now parking cost is "units per tenth of a dollar" while fare is still "units per dollar".
Is the correct way to treat this, when I'm presenting them, to divide the parking cost utility by 10 to show it in "units per dollar"? So the parking cost would be -12.05, not -120.46? Or is that skipping assumptions that were made in the zero-centring of the results? I'm happy to clarify if this didn't make sense, hope my question is clear! Thanks :)
Update: I chatted a bit with support, I'm assuming you can't actually do this because you're scaling each set of utilities differently? Like if I was do divide parking cost by 10 I would need to do this for every alternative. Ultimately my solution still converges well in the initial case I had, so I would assume that I just accept that my range is quite wide and stick to my initial scenario? I think the values go up to 30 at most across all my variables, and go as low as 1, so not an easy range of values to compress into ~0.3-10