No priors

[Sanchez]

Our project will be examining the visual disamenities of structures which are at different distances from a touristic viewpoint (there is a fee to access this viewpoint). The number / size of the structures is also varied. Respondents are asked what price discounts they would be willing to accept to face the new view (with structures in the viewshed). As such, my three variables are distance (dist – 5,8,12,18miles), size (small and large) as well as price (+5%, 0%, -5%, - 10%, - 15% -25%).

The only studies similar to ours have been done in different countries and are not similar enough in nature to use their coefficient estimates as priors. As such, besides knowing that the signs on both the distance and price attributes are negative, I have no information regarding priors. As such, I see two options, but I don’t know which is superior:

Option 1: One alternative would be (as recommended to Doug on the Ngene forum on March 28, 2009 (Topic: Large Experimental designs)), to generate an orthogonal design for a pilot study first and then use the priors obtained during that study to generate an efficient design.

What sample size pilot study would one need to develop a prior (given that my minimum sample size is around 200)? i.e. what percentage of the final, minimum sample size needed to generate accurate choice probabilities is needed for a pilot?

Option 2: On page 93 of the manual it mentions that any amount of information is better than using no prior information as in an orthogonal design. As mentioned, I do claim to know that the signs of both price and distance are negative. How do I incorporate that into the design? Instead of using zeros as in the following design, should I rather make a very small negative number such as -0.0001? Furthermore, would it still be worth it to run a focus group, even if such a design was obtained?

Your help would be greatly appreciated.
Sanchez

p.s. Here is the syntax I created for the options above.

Option 1:
Design
;alts = alt1, alt2
;rows = 36
;orth = sim
;block = 6
;model:
U(alt1) = b2*dist[8,12,18,5] + b3*size[144,64] +b4*price[-5,5,10,15,25,0] +b5*dist*size /
U(alt2) = b2*dist + b3*size +b4*price
$

Option 2:
Design
;alts = alt1,alt2,sq
;rows=12
;block=2
;eff=(mnl,d)
;alg = mfederov
;model:
U(alt1) = b2.effects[0|0|0]*dist[8,12,18,5] + b3.effects[0]*size[144,64] +b4[0]*price[-5,5,10,15,25,0] /
U(alt2) = b2*dist + b3*size +b4*price
$

p.s.s How long does is typically take to find a design? I ran option 2 and after 3 hours and over 10 000 000 iterations, I had still not found a single design.

[johnr]

Hi Sanchez

To answer your specific questions

1. We typically use sample sizes of 10-15 respondents for the pilot. Provided you are not going to change the attributes and levels, these can be used in the final sample so it does not necessarily affect your final sample.

2. You can use Bayesian prior parameter distributions rather than exact priors (local priors). If you know the sign for example, you could use a Bayesian uniform prior between say -1 and 0 (note that this is an example and you should use values that reflect the likely magnitudes of the parameters to be estimated). This will optimise the design over the range of potential parameters included in the assumed distribution. If you do not know the sign for example, you can do the same, but use a uniform over the range of say -1 and 1 (again, an example only and the range should reflect the expected parameter magnitudes of the parameter).

Note that 1 and 2 are not mutually exclusive. Some prefer to use an orthogonal design for the pilot. I prefer to use a Bayesian efficient design. One approach however need not be considered better than the other.

Regarding the designs, I generated the optimal design for the first syntax in less than 4 seconds. The second design will continue to run until you stop it, however it generated designs almost instantaneously after I pressed run. A description on how to access the design is given in Section 3.4. Can you confirm that there are no designs in what you have done.

John

[Sanchez]

Hi John.
Thank you very much for answering those questions - that helps a lot!
Also - after reading your mail, I do now see that I did get designs. Although I read the manual, I was confused about the program continuing to run. Thank you for clearing that up for me!
Thanks again.
Sanchez