Realistic efficient designs with prices and quantities

[mquaife]

Hi,

I am designing a v simple task where people choose their favourite food shopping baskets, hoping to predict substitution patterns from price changes. I therefore need to show respective product quantities and associated prices in each task, and need to estimate a price parameter and parameters for each food type (say maize, rice, fish). If quantities for each food type can be 0,1,2, I need price to be dependent on the quantity. I have explored the following NGENE options:

1) separate price and quantity parameters, using conditional statements to restrict prices according to quantity => too many parameters, huge (but perhaps meaningless?) Sp value for our sample size

e.g. U(A)=rice.effects[0|0]*rice[0,1,2]+rice_price[0]*rice_price[0,3,6] + same for maize, other products

2) having levels of product=the price of that product. E.g. rice[$0,$3,$6] then reverse engineering the design such that I infer if the quantity was 0,1(if attribute was $3),2(if attribute was $6) bags of rice, then recovering the price of the basket through summing the levels of each outside of NGENE. In piloting, this has resulted in a v meaningless price coefficient, presumably since the "global" parameter basket price (=sum of attribute levels in an alternative) is not in the design.

We also have a condition that the total price of the basket should be something reasonable. I am posting syntax of this second option below (prices varying from the above due to currency).

This feels like it should be a really simple task to design - am I missing something obvious here? Would appreciate any insights

All the best,
Matt

Design
;alts=A,B,C
;rows=5
;eff=(MNL,d)
;alg = mfederov(candidates=2000000)
;reject:
A.maize_price+A.cabb_price+A.rice_price+A.fish_price+A.chips_price>1100,
B.maize_price+B.cabb_price+B.rice_price+B.fish_price+B.chips_price>1100,
C.maize_price+C.cabb_price+C.rice_price+C.fish_price+C.chips_price>1100,
A.maize_price+A.cabb_price+A.rice_price+A.fish_price+A.chips_price<800,
B.maize_price+B.cabb_price+B.rice_price+B.fish_price+B.chips_price<800,
C.maize_price+C.cabb_price+C.rice_price+C.fish_price+C.chips_price<800

;model:

U(A)=maize_price[0.1]*maize_price[0,150,300,450,600]+
cabb_price[0.1]*cabb_price[0,150,300]+
rice_price[0.1]*rice_price[0,250,500]+
fish_price[0.1]*fish_price[0,150]+
chips_price[0.1]*chips_price[0,200]
/
U(B)=maize_price[-.1]*maize_price[0,150,300,450,600]+
cabb_price[0.1]*cabb_price[0,150,300]+
rice_price[0.1]*rice_price[0,250,500]+
fish_price[0.1]*fish_price[0,150]+
chips_price[0.1]*chips_price[0,200]
/
U(C)=maize_price[0.1]*maize_price[0,150,300,450,600]+
cabb_price[0.1]*cabb_price[0,150,300]+
rice_price[0.1]*rice_price[0,250,500]+
fish_price[0.1]*fish_price[0,150]+
chips_price[0.1]*chips_price[0,200]

$

[Michiel Bliemer]

While it seems a simple design, there is a bit more to it I think.

There are actually two choices being made by the respondent, namely:

* Choice 1: Product choice
* Choice 2: The amount to buy

The second choice is often a continuous choice, and this would fit within the discrete-continuous choice model framework.

Choice 1 would be a typical stated choice survey, which choice tasks that consist of attributes like brand and price per liter or gram (in which the price is normalised to take out the quantity). Choice 2 depends on family size, time frame, etc.

Maybe you could in the survey first found out what quantity households buy (per day, week, or month?), and then tailor your choice tasks around this quantity such that all products have the same quantity in order to make it a fair choice.

Michiel

[johnr]

Hi Matt

Your problem is not a discrete choice problem per se. As Michiel stated, it is a discrete-continuous problem: discrete in that you have discrete products people can choose, continuous in terms of they can select multiple amounts from more than one discrete alternative.

From a modelling perspective, you can use MCDEV type models for this data, or depending on how you collect the continuous amounts, you can use another approach. In Ardeshiri and Rose (2017), we had 7 alternatives but each respondent saw only 4 of these in any one task. Respondents could choose 0,1 2 3, or 4+ of any (multiple) alternative(s).We modelled each alternative as separate ordered logits, but allowed substitution effects via an error component structure.

A Ardeshiri, JM Rose (2017) How Australian consumers value intrinsic and extrinsic attributes of beef products, Food Quality and Preference

However that is modelling, not design. I have been working on an optimal design approach for this problem in between other things, however not anywhere near ready. For the paper, we just optimised on the discrete component of the model to generate the design using existing approaches.

Some thoughts on your post. You state that you get large Sp sample requirements. This is likely due to your priors, than the problem itself. n_k => (t_k^2*se_k^2)/beta__k^2. Given beta__k^2 is in the denominator, as it approaches zero, n_k increases. This makes sense. If the true parameter is close to zero, you will generally need a larger sample size to detect a significant difference from zero. This doesn't really have anything to do with number of parameters - just the values you assumed for them.

John

[mquaife]

Thank you John and Michiel, useful insights from you both.

John - I missed your message before we had to go into the field, but we ended up optimising on the discrete component as you also did. Will be really interested to hear about developments in discrete-continuous designs.

Best wishes
Matt