Availability design

[paulm]

Hello,

I would like to create an availability design. This type of design is often used when assessing the potential for new products entering a market. The availability design contains estimable cross effects, which are a useful way to remove the effect of IIA in logit models.

Here is a stylized example:
design
;alts = existing1, existing2, new, none
;eff=(mnl,d)
;model:
u(existing1) = b10 + b11*feature1_1[1,2,3] + b12*feature2_1[1,2,3] + b13*feature3_1[1,2,3,4] + ... /
u(existing2) = b20 + b21*feature1_2[1,2,3] + b22*feature2_2[1,2,3,4] + b23*feature3_2[1,2,3,4] + ... /
u(new) = b30 + b31*feature1_3[1,2,3] + b32*feature2_3[1,2,3,4] + b33*feature3_3[1,2,3,4] + ...
$

What is different here is that we want the "new" product to appear in the choice task only part of the time (say 8 times out of 12). So sometimes, there would be 4 choices available and sometimes only 3.

There are several ways to accomplish this.

Method 1: add an additional level to one attribute associated with "new". Treat that attribute as "not available" and zero out the full column when that attribute level comes up. With orthogonal designs, thsi generally works and all main effects are estimable, as are the availability cross effects. It helps to have an attribute avaialable with the right number of levels so that adding the extra one makes "not available" turn up the right number of itmes.

Method 2: add an additional attribute to "new" for availability. With orthogonal designs, we might give it levels 1, 2 and 3 where 1 and 2 are available and 3 is not, to create the desired imbalance. Or imbalance constraints could be used.

Metohd 3 (not generally recommended): add an additonal level to all attributes, with if-and-only-if constraints so that either all attributes are at the added level or none are. Generally, this doesn't provide the balance desired, so it's not so useful.

Ok, so this type of thing has been used with reasonable effect in orthogonal designs, where all priors are 0. But what about efficient designs with priors? How do you place a prior on "not available" since there's no actual parameter estimated for that? How do you place priors on the cross effects (if you have any)? And how would you implement this type of design in NGene?

Thanks much.

Paul

[johnr]

Dear Paul

We have recently programmed availability designs with the aim of releasing the code in a future version of Ngene. We have several options for doing so.

1. The availability design is orthogonal
2. The availability design is a BIBD design
3. The availability design is an efficient design

The benefit of 2 and 3 is that you can specify that all choice tasks will have the same number of alternatives (not possible with 1), whilst 3 will also allow you to specify the variable choice set sizes. As such, it is more flexible. Approach 2 is neat in that each alternative will be paired against each other alternative an equal number of times, however it there are few known BIBDs so it is somewhat limited to very specific problems.

The new code will also allow users to specify manually which alternatives will be in/out of specific choice tasks.

These availability designs (whether 1,2 or 3) are simply binary levels where an alternative will be either present/absent from a choice task (hence you have one column per alternative).

Given an alternative is present (via the availability design), the software will then generate the levels for the alternative.

As such, you actually will have two designs. The availability design dictating presence/absence of an alternative and the sub-design which picks the levels of present alternatives.

We are hoping to present these designs at a conference later this year (we have submitted an abstract, will find out hopefully this week whether it is accepted or not and if not we will simply submit it to a journal), none of which helps you.

To assist, I'm happy to generate the design for you. You can be our guniea pig if you are willing. Drop me an email as I need more information to generate the design for you (john.rose@sydney.edu.au)

John