Design with all attribute levels continuous

[prefer]

Dear Ngene users and admins

I am trying to make a simple CE design with two alternatives and two attributes. The attributes are the amount of powder in gram (250g, 150g, 50g, 0g) and price (35,37,39,43,44,47). I want to generate a design with all attribute levels continuous.

When running the following design, I got an unrealistically very high D-error (2848580748.688759) and the attribute levels are the same in both alternatives. Would you be so kind in sharing your views as to what I should do to improve the design? Thank you!

[Design
; alts = alt1, alt2, alt3
; rows = 12
; eff = (mnl,d)
; Model :
U(alt1) = amo[1.2]*amount[250,150,50,0]+cost[-0.001]*price[35,37,39,43,44,47]/
U(alt2) = amo*amount+cost*price$]

Kind regards
Mame

[prefer]

When I change the priors for the amount attribute from 1.2 to 0.2 then I got a much lower D-error which is fine. However, the attribute levels for the amount attribute are the same in both alternative for all choice situations.

[prefer]

Now I tried changing the attribute levels for 'amount' to something like [1,2,3,4], and in this case the design works. I think the problem lies on defining the levels as [0,50,150,250]. I have some questions though:

1) should I consider using the 'cond' property in order to avoid the problem of identical levels in different alternatives?
2)or should I consider using a design with continuous attribute levels as described in Ngene manual?
3)or should I just go on just by specifying the levels as 1,2,3,4?

Thank you indeed.
Mame

[Michiel Bliemer]

Your prior for amo is problematic and unrealistic. If you have an attribute with levels ranging from 0 to 250 and a prior of 1.2, then the different in utility between an alternative with level 0 and an alternative with level 250 is 250*1.2, which is extremely large and completely dominant. Ngene will in this case try to get the levels across alternatives as close as possible. If you would have used a continuous level, you would probably end up with alternatives with attribute levels 249 and 250 grams, such that the difference between utilities is 1*1.2, which is more reasonable. So your outcomes can easily be explained.

Please make sure that your prior makes sense and comes from either literature or (preferably) from a small pilot study.

Setting all attribute levels constant is typically not useful, as this will lead to an end-point design for most attributes (using only the upper and lower bound) while for one attribute the level will not be at the extreme ends. So usually it suffices to use only a single continuous attribute with continuous levels. When you use continuous levels, it is very important that you have very good and reliable priors, but I am not sure if that is the case here.

Michiel

[prefer]

Dear Michiel,

Thank you for the advice and I realize the problem. I am just making the design just using my own priors to make simulation, and as you said the priors are not reliable and I can see that when I change the priors. The design will be used for a pilot study and for that I will use 0 as a prior and then use the results from the pilot as priors to produce the final design.

However, we decided to make the amount attribute continuous and investigate the linear relationship, simply because it doesn't make sense to make the amount attribute dummy/effects coded variable while it is a continuous variable - it is continuous in a sense that its levels are 250g,150g,50g,and 0g. So what I am thinking now is to use 1,2,3,4 as levels of the amount attribute in the design and replace these levels with 250,150,50 and 0 later on as it is commonly done when designing a DCE. Do you see any problem in doing that?

For you information, I got the following design (the design code is copied) but I am a little bit suspicious of the choice probabilities. Do you think they are OK? And attribute level 1 is identical in choice situation 2 and 6 for the amount attribute? I don't think that a problem but do you see any noise? Thank you indeed for your time!!

Design
; alts = alt1, alt2, alt3
; rows = 12
; eff = (mnl,d)
; Model :
U(alt1) = amo[0.95]*amount[1,2,3,4]+cost[-0.006]*price[35,37,39,43,44,47]/
U(alt2) = amo*amount+cost*price$

MNL efficiency measures

D error 0.011823
A error 0.089087
B estimate 25.032272
S estimate 105.201374

Prior amo cost
Fixed prior value 0.95 -0.006
Sp estimates 0.754224 105.201374
Sp t-ratios 2.256867 0.191093

Design
Choice situation alt1.amount alt1.price alt2.amount alt2.price
1 3 39 1 43
2 1 47 1 44
3 2 39 4 37
4 1 43 3 39
5 4 35 3 44
6 1 44 1 47
7 4 37 2 39
8 2 47 3 35
9 3 44 4 35
10 4 37 2 43
11 3 35 2 47
12 2 43 4 37

MNL probabilities
Choice situation alt1 alt2 alt3
1 0.820266 0.119777 0.059957
2 0.395117 0.402293 0.20259
3 0.125697 0.850546 0.023757
4 0.119777 0.820266 0.059957
5 0.717355 0.262847 0.019798
6 0.402293 0.395117 0.20259
7 0.850546 0.125697 0.023757
8 0.251443 0.698697 0.04986
9 0.262847 0.717355 0.019798
10 0.853088 0.123084 0.023828
11 0.698697 0.251443 0.04986
12 0.123084 0.853088 0.023828

[Michiel Bliemer]

A couple of comments:

1. You mentioned 'continuous attribute levels', but you actually mean 'linear relationships'. The utility function you are using is referred to as LPLA (linear in parameters, linear in attributes). That was the confusion. Dummy/effects coding refers to nonlinearities.So your utility function is fine.

2. You have specified the alternatives as labelled, so it thinks that (44,47) is different from (47, 44). If you mean unlabelled alternatives, you should use ;alts = alt1*, alt2* (putting an asterisk behind the unlabelled alternatives).

3. You did not specify a utility function for alt3, so it is considered to be the no-choice alternative. You did not specify any constants, so the utility for this alternative is assumed to be zero, but this may not be consistent with alt1 and alt2. So you may wish to add a constant.

4. The probabilities are meaningless if your priors are not correct, and if your attribute levels are not the ones that you use in estimation. You cannot simply changes them and look at the probabilities or even the D-error. In case you do not know the priors, please use zeros, or a small value with the proper sign.

[prefer]

Dear Michiel,

OK thank you for your advises, I will employ them. I want to make my design unlabelled and alt3 is the no-choice option, that is why I didn't specify a utility function for it. I will put an asterisk behind alt1 and alt2 but but not behind alt3.