Dominat alternatives for fixed prior

[wxy008]

Dear Ngene experts,

I run an efficient design (Codes shown below) and got 99.6 of B estimate. However when I check the result and found there were a lot alternative pairs of same price with different combination of other attributes. For example:

Design
Choice situation alt1.price alt1.or alt1.ft alt1.ct alt2.price alt2.or alt2.ft alt2.ct Block
1 9.95 0 0 0 9.95 0 1 1 4
2 9.95 1 1 1 9.95 0 1 0 2
3 9.95 0 0 0 9.95 1 0 1 1
4 12.45 0 0 1 12.45 0 1 0 3
5 7.45 0 0 1 7.45 0 1 0 1
6 12.45 0 0 0 12.45 0 0 1 1
7 9.95 0 1 1 9.95 1 1 0 1
8 4.45 0 0 1 4.45 1 1 1 4
9 9.95 0 0 0 9.95 0 1 0 3
10 9.95 0 0 1 9.95 0 0 0 2
11 7.45 1 1 1 7.45 0 1 1 2
12 4.45 0 1 0 4.45 0 1 1 3

Is this ok? or something wrong in codes? If so, how can improve this?
The Ngene codes are listed below:

Code: Select all

Design;
;alts = alt1*,alt2*,nobuy
;rows = 32
;eff = (mnl,d)
;alg = mfederov
;block = 4
;model:
U(alt1) =  b0 + b1[-0.01] * price[4.95, 7.45, 9.95, 12.45](8,8,8,8) +
                 b2.dummy * Or[0,1] +
                 b3.dummy * Ft[0,1]  +
                 b4.dummy * Ct[0,1]
                         /
U(alt2) = b0 + b1     * price +
                 b2         * Or +
                 b3        * Ft +
                 b4         * Ct
 
$


Thanks so much for your help.

Wei

[Michiel Bliemer]

If you use dominance checks, you need to use non-zero priors for all or most attributes, for example, I guessed the signs of the priors in the syntax below, but please change so that they reflect the correct sign. You cannot apply dominance checks while providing the sign of only one of the priors. If you do not know the sign of the other priors, then there should be no obvious dominance issues and you can remove the dominance checks, i.e. use ;alts = alt1, alt2.

Code: Select all

Design;
;alts = alt1*,alt2*,nobuy
;rows = 32
;eff = (mnl,d)
;alg = mfederov
;block = 4
;model:
U(alt1) =  b0 + b1[-0.01] * price[4.95, 7.45, 9.95, 12.45](8,8,8,8) +
                 b2.dummy[-0.01] * Or[0,1] +
                 b3.dummy[0.01] * Ft[0,1]  +
                 b4.dummy[-0.01] * Ct[0,1]
                         /
U(alt2) = b0 + b1     * price +
                 b2         * Or +
                 b3        * Ft +
                 b4         * Ct
 
$

This generates:

Choice situation alt1.price alt1.or alt1.ft alt1.ct alt2.price alt2.or alt2.ft alt2.ct Block
1 4.95 0 0 1 4.95 1 1 0 3
2 12.45 0 0 0 4.95 1 1 1 1
3 7.45 0 1 0 9.95 1 0 1 1
4 7.45 0 1 0 12.45 1 0 1 4
5 12.45 1 0 1 9.95 0 1 0 1
6 9.95 1 1 0 4.95 0 0 1 3
7 12.45 1 1 1 12.45 0 0 0 1
8 7.45 1 0 0 9.95 0 1 1 2
9 4.95 1 0 0 9.95 0 1 1 2
10 7.45 1 1 1 12.45 0 0 0 4
11 9.95 1 0 1 4.95 0 1 0 3
12 9.95 0 0 1 12.45 1 1 0 1
13 12.45 0 1 1 7.45 1 0 0 3
14 12.45 0 0 0 9.95 1 1 1 2
15 4.95 0 1 0 7.45 1 0 1 3
16 4.95 0 0 1 7.45 1 1 0 2
17 4.95 1 0 0 7.45 0 1 1 1
18 7.45 1 1 1 9.95 0 0 0 1
19 4.95 0 0 0 7.45 1 1 1 2
20 4.95 1 0 0 12.45 0 1 1 4
21 4.95 0 0 1 12.45 1 1 0 2
22 7.45 1 0 0 4.95 0 1 1 2
23 7.45 0 0 0 7.45 1 1 1 2
24 9.95 0 0 1 4.95 1 1 0 3
25 12.45 1 1 0 7.45 0 0 1 3
26 9.95 1 0 0 12.45 0 1 1 4
27 12.45 1 0 1 4.95 0 1 0 3
28 7.45 0 0 0 4.95 1 1 1 4
29 9.95 0 0 0 9.95 1 1 1 1
30 9.95 0 0 1 9.95 1 1 0 4
31 12.45 0 0 1 12.45 1 1 0 4
32 9.95 1 0 0 7.45 0 1 1 4

Michiel

[wxy008]

Michiel,

Thanks so much for your help. Could you explain why there is no bovious dominace issues if i do not know the sign of the other priors? also if I use ;alts= alt1,alt2, how does no buy option affect design? does this change ulabeled design to labeled design?

Wei

[Michiel Bliemer]

Consider for example two attributes, price and quality. I know that price has a negative coefficient and quality a positive. Having this knowledge, Ngene knows that ($1, high quality) is dominant over ($2, low quality). But if you do not provide signs, then it is not possible to check for dominant alternatives, as dominance can only be determined if we know that one attribute level is better or worse than another attribute level. So with zero priors, one cannot do dominance checks. Please refer to Bliemer et al. (2017), which provides the underlying theory for dominance checks based on regret theory.

Bliemer, M.C.J., J.M. Rose, and C.G. Chorus (2017) Detecting dominance in stated choice data and accounting for dominance-based scale differences in logit models. Transportation Research Part B, Vol. 102, pp. 83-104.

While price and quality have clear signs, some attributes do not have an obvious prior, for example colour package (red, blue, green) and flavour (chocolate, vanilla). Is (red, chocolate) dominant over (green, vanilla)? Here it is likely that you would not need to do dominance checks because there is no clear ordering of the levels and you could set zero priors and remove dominance checks.

You have decide for your attributes whether there exists a natural ordering or not.

The optout alternative allows you do estimate a model where price is equal across alt1 and alt2, whereas if there is no optout this is not possible because the price parameter will not be identifiable. Also, if you have no optout you would not estimate constant b0.

Michiel

[wxy008]

Thanks so much, Michiel.

Wei