Questions about the priors

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Questions about the priors

Postby Rim » Tue Apr 02, 2019 4:52 am

Hello,

I am working on an efficient design where the respondent has a statusquo and makes a choice between 4 alternatives (his status quo and 3 other alternatives) : Car, Public Transport , Bicycle and Walking. The alternatives are described by 4 attributes: time, cost, an individual preceived mobidity risk (physicalactivity) and a population morbidity risk(pollution).
I have 2 questions regarding the priors. I did not have time nor the budget to make a pilote, so I did a literature review and some personal assuptions to define the priors.

1- Through the literature review, I defined an interval of Value Of Time. From this interval I wanted to calculate the interval of the priors of time. I supposed that beta cost= -0,1 which allowed me to have the priors for time b1[(u,-0.05,-0.0017)]. At this level, wanting to introduce the priors for cost in my design I did not know what to do. Should I put a fixed prior b2[-0.1] following the assuption above? Or should I introduce an interval for this attribute giving ngene the information aout the sign that I am expecting for this attribute (for example a negative prior b2[(u,-0.1,-0.001)] for cost since higher cost is perceived negaively)? If It's an interval for priors of cost, should it be a large interval or a small one close to 0?

2- For the attributes about morbidity (physicalactivity and pollution), I could not find enough reliable sources to create an intervals of priors. The only information that I have is that the sign is negative (a risk of morbidity is perceived negatively). To express this information, I introduced negative priors b3[(u,-0.2,0)] and b4[(u,-0.2,0)]. Are these priors good enough for my situation? should I make the intervals larger or smaller?

Here is an example of my code for a respondent with a statuquo using the car:

Design
Design
;alts= Car, PT, Bicycle, Walk
;rows=21
;eff = (mnl,d)
;block=3
;model:
U(Car) = b1[(u,-0.05,-0.0017)]* Time.ref[4]
+ b2[-0.1] * Cost.ref[0.5]
+ b3[(u,-0.2,0)] * physicalactivity.ref[0.3]
+ b4[(u,-0.2,0)] * pollution.ref[0.3]/


U(PT) = b1* Time[5, 7, 9]
+ b2 * Cost[0 , 0.50 , 1.50]
+ b3 * physicalactivity[0.24, 0.26, 0.28]
+ b4 * pollution[0.27, 0.28, 0.29] /

U(Bicycle) = b1* Time[5, 6, 8]
+ b2 * Cost[0]
+ b3 * physicalactivity[0.24, 0.26, 0.28]
+ b4 * pollution[0.25, 0.26, 0.27] /

U(Walk) = b1 * Time[7, 10, 12]
+ b2 * Cost[0]
+ b3 * physicalactivity[0.20, 0.24, 0.27]
+ b4 * pollution[0.25, 0.26, 0.27]
$


Thank you in advance for your time and help.
Rim.
Rim
 
Posts: 6
Joined: Tue Dec 11, 2018 8:32 pm

Re: Questions about the priors

Postby Michiel Bliemer » Tue Apr 02, 2019 3:07 pm

1. I think that you will find the paper below interesting to look it. It describes how you could determine priors without a pilot study but rather by judging yourself in a systematic way. In particular you will need to think about the scale of your parameters.

Bliemer, M.C.J., and A.T. Collins (2016) On determining priors for the generation of efficient stated choice experimental designs. Journal of Choice Modelling, Vol. 21, pp. 10-14.

2. Using Bayesian priors like this to indicate a negative prior is fine. I cannot comment on the actual value of -0.2 without doing a pilot study or going through an expert judgement process as described in the paper above.

Michiel
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Re: Questions about the priors

Postby johnr » Tue Apr 02, 2019 3:18 pm

Hi Rim

You logic is sound, though there are some side effects from your approach that you might need to consider. The magnitude of parameters from a model will be proportional to the values of the Xs. If you rescale the Xs (say divide by 1000), then the parameters will automatically rescale so that the overall outcome (utility) remains the same. You have assumed a VoT of between $1.02 and $30 per hour which is fine, however these seem very high given you have travel times between 4 and 12 minutes. The theory of VoT suggests that it should increase with longer travel times (see Jara-Díaz, S. (2008) Transport Economic Theory, p61). Anyway, putting that aside, the consequences of your approach are as follows.

1) Consider the impact on utility at the average attribute level. For simplicity, lets just take the mid points. For travel time (4-12) = 8, cost (0-1.5) = 0.75, physical activity (0-0.28) = 0.14, and pollution (0-0.29) =0.145.

2) Now consider the midpoint of the parameters. For travel time (-0.0017- -0.05) = -0.02585, cost (-0.1) = -0.1, physical activity (0 - -0.2) = -0.1, and pollution (0 - -0.2) = -0.1.

3) With 1) and 2) we can get an idea of the average (or thereabouts) impact on utility for each attribute.

Time = -0.02585*8 = -0.2068
Cost = -0.1*0.75 = -0.075
Physical activity = -0.1*0.14 = -0.014
Pollution = -0.1*0.145 = -0.0145

Whilst this is very rough, it does give us an indication as to the relative importance you are assigning to each attribute on utility given the priors you selected. For example, time is 14.771 times more important than say physical activity at the averages assumed. This is not a bad thing, but something that you might want to be aware of. It also explains the high S-errors (indicating sample size requirements) for physical activity and pollution. Both attributes have almost no impact on utility compared to time and cost - in fact, time and cost are dominating utility. This may be the case, and the priors should represent this fact, however it is a consequence of the priors you have assumed and you should be aware of this. It basically means that the last two attributes will probably never be statistically significant in any meaningful sample you will collect. Again, this may be true, but you should be aware of this.

John
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Re: Questions about the priors

Postby Rim » Thu Apr 04, 2019 6:27 pm

thank you both for your responses, I appreciate it!

Rim.
Rim
 
Posts: 6
Joined: Tue Dec 11, 2018 8:32 pm


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