Correct if all the utilities of alternative1 and 2 negative?

[qwdl]

Dear Experts,

I am using a D-efficient design. After the pilot, I got all the priors. In each choice set, I have three alternatives, option 1, option 2, and opt-out. After I ran the formal design, I have two attributes that have negative priors, which are also in line with the theory. Then I found that the utilities of option 1 and option 2 in all choice sets are all negative in the formal design. Is that correct? Can all the utilities of option 1 and 2 negative? Now the prior of constant is zero. If I give the constant a negative constant, can all the utilities of option 1 and 2 negative?

The code in ngene now is
Design
;alts=alt1*,alt2*,alt3
;rows=24
;block=4
;eff=(mnl,d)
;model:
U(alt1)=b1[-0.0021]*A[130,170,210]+b2.effects[0.2820|0.1262]*B[2,1,0]+b3.effects[0.0801|0.0559|0.1172]*E[3,2,1,0] +b4[-0.0511]*C[12,15,18]+b5[0.003]*D[50,60,70]+/
U(alt2)=b1*A+b2*B+b3*C+b4*D+b5*E/
U(alt3)=b0[0]
$


Thanks so much!

[Michiel Bliemer]

Yes utilities can be negative, only DIFFERENCES IN UTILITY matter.

For example, these utilities
U(alt1) = -3
U(alt2) = -2
U(alt3) = -1

result in the same choice probabilities as these utilities:
U(alt1) = 5
U(alt2) = 6
U(alt3) = 7

and these choice probabilities:
U(alt1) = -2
U(alt2) = -1
U(alt3) = 0

Note that you should NOT just set the constant for b3 to zero, you should estimate a prior for this constant using your pilot study data, assuming that you also had an opt-out alternative in your pilot study.

Michiel

[qwdl]

Dear Prof.Michiel Bliemer,

Thank you so much for your reply! I have an opt-out in the pilot. Then how to estimate the constant? I used logit and conditional logit in stata to run the pilot model.

The logit model shows as belows:
coef.
attribute1 -0.0021
attribute2 0.2077
attrubute3 -0.415
...
attrubute6 0.0566
_cons -2.62

Should I use -2.62 in the estimated logit model as the prior of the constant b3?

The conditional logit (asclogit) shows as belows:
alt coef.
attribute1 -0.0031
attribute2 0.3079
attrubute3 -0.567
...
attrubute6 0.0766
1 base alternative
2 _cons -0.085
3 _cons -2.654 (here 3 represent opt-out)
Should I use -2.654 in the estimated conditional logit model as the prior of the constant b3?

Thanks so much!

[Michiel Bliemer]

I do not know how choice model estimation in stata works, but it seems it estimates two constants (relative to alt1) and then indeed it would be -2.654.

Michiel

[qwdl]

Dear Prof.Michiel Bliemer,

Thanks so much!


Best!