## Minimum number of choice situations and SQ

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### Minimum number of choice situations and SQ

I’m preparing a design for an unlabelled choice experiment with 2 alternatives and a statu-quo. The status-quo levels are fixed and present in the other two alternatives for all attributes except the monetary attribute which level is 0 in the status quo and superieur to 0 in the alternatives. My code is the following:

Design
;alts=alt1, alt2, sq
;rows=?
;block=?
;eff=(mnl,d)
;alg = mfederov(candidates = 500)
;require:
sq.INF = 1,
sq.HEAT = 1
sq.CAR = 1,
sq.DISTANCE = 1

;model:
U(alt1)=b1.dummy[0|0|0|0]*INF[1,2,3,4,5] ? INF : Water substitution level INF=1 <10% INF=2 25% INF=3 50% INF=4 75% INF=5 100%
+b2.dummy[0|0|0|0]*HEAT[1,2,3,4,5] ? HEAT : Heat island effect surface reduction HEAT=1 0% HEAT=2 15% HEAT=3 30% HEAT=4 45% HEAT=5 60%
+b3.dummy*CAR[1,2] ? CAR Reduction of road and parking space CAR=1 No Reduction CAR=2 Reduction
+b4.dummy[0|0|0|0]*DISTANCE[1,2,3,4,5] ? DISTANCE Distance of closest solution to home DISTANCE=1 No new green solution DISTANCE=2 100m DISTANCE=3 200m DISTANCE=4 500m DISTANCE=5 1KM
+b5*BILL [10,20,30,40, 50] ? Increase of the water bill in €
U(alt2)=b1*INF+b2*HEAT+b3*CAR+b4*DISTANCE+b5*BILL
U(SQ)= b6+ b1*INF+b2*HEAT+b3*CAR+b4*DISTANCE
\$
I have 3 questions:
- Is my coding of the status-quo accurate?
- I'm struggling with the estimation of the minimum of choice situation. In the formula used to estimate the minimum number of choice situation, (J-1)S=K I wonder whether the status quo is considered an alternative. In other words, if J=2 or 3. If the SQ is not an alternative then K being equal to 15 (including constant). I have to include a minimum of 15 choice situations, 20 if I want to have attribute level balance. If the SQ counts then the minimum number is 7.5 and we can live with 10 choice situations.
- If I end up with 20 choice situations. Is it preferable to have 2 blocks of 10 or 4 blocks of 5.

Thanks a lot for your help
p.lecoent

Posts: 8
Joined: Tue May 10, 2022 1:59 am

### Re: Minimum number of choice situations and SQ

Yes you have coded the status quo alternative correctly. I have added "/" after each alternative and I added attribute level constraints for the numerical attribute BILL since the modified Federov algorithm does not satisfy attribute level balance.

SQ is an alternative, so you would at minimum 8 choice tasks to estimate the model. It is a good idea to have more variation in your data, so I generally recommend multiplying this theoretical minimum with 2 or 3, so in your case 20 should be fine. If you believe that respondents will be able to handle 10 choice tasks, then 2 blocks is best, but if you believe this is too demanding then you may need to use 4 blocks.

The script below would work.

Code: Select all
`Design;alts=alt1, alt2, sq;rows=20;block=2;eff=(mnl,d);alg = mfederov(candidates = 500);require:sq.INF = 1,sq.HEAT = 1,sq.CAR = 1,sq.DISTANCE = 1;model:U(alt1) = b1.dummy[0|0|0|0] * INF[1,2,3,4,5]                             ? INF : Water substitution level INF=1 <10% INF=2 25% INF=3 50% INF=4 75% INF=5 100%        + b2.dummy[0|0|0|0] * HEAT[1,2,3,4,5]                            ? HEAT : Heat island effect surface reduction HEAT=1 0% HEAT=2 15% HEAT=3 30% HEAT=4 45% HEAT=5 60%        + b3.dummy       * CAR[1,2]                                   ? CAR Reduction of road and parking space CAR=1 No Reduction CAR=2 Reduction        + b4.dummy[0|0|0|0] * DISTANCE[1,2,3,4,5]                        ? DISTANCE Distance of closest solution to home DISTANCE=1 No new green solution DISTANCE=2 100m DISTANCE=3 200m DISTANCE=4 500m DISTANCE=5 1KM        + b5             * BILL [10,20,30,40,50](2-4,2-4,2-4,2-4,2-4) ? Increase of the water bill in €, added attribute level constraints to ensure some degree of balance for numerical attribute        /U(alt2) = b1*INF + b2*HEAT + b3*CAR + b4*DISTANCE + b5*BILL /U(SQ)   = b6 + b1*INF + b2*HEAT + b3*CAR + b4*DISTANCE\$`

If you want to have attribute level balance in your design, you need to use the default swapping algorithm. Note that the LAST level in Ngene is the reference level for dummy coding, so I have moved level 1 to the end of levels. This means that level 1 is the base for all dummy coded attributes and therefore adds 0 utility for this level. This means it can be left out of the status quo alternative and no require constraints are necessary. The script below will generate the design.

Code: Select all
`Design;alts=alt1, alt2, sq;rows=20;block=2;eff=(mnl,d);model:U(alt1) = b1.dummy[0|0|0|0] * INF[2,3,4,5,1]         ? INF : Water substitution level INF=1 <10% INF=2 25% INF=3 50% INF=4 75% INF=5 100%        + b2.dummy[0|0|0|0] * HEAT[12,3,4,5,1]       ? HEAT : Heat island effect surface reduction HEAT=1 0% HEAT=2 15% HEAT=3 30% HEAT=4 45% HEAT=5 60%        + b3.dummy       * CAR[2,1]               ? CAR Reduction of road and parking space CAR=1 No Reduction CAR=2 Reduction        + b4.dummy[0|0|0|0] * DISTANCE[2,3,4,5,1]    ? DISTANCE Distance of closest solution to home DISTANCE=1 No new green solution DISTANCE=2 100m DISTANCE=3 200m DISTANCE=4 500m DISTANCE=5 1KM        + b5             * BILL [10,20,30,40,50]  ? Increase of the water bill in €        /U(alt2) = b1*INF + b2*HEAT + b3*CAR + b4*DISTANCE + b5*BILL /U(SQ)   = b6 + b5*BILLsq\$`

Michiel
Michiel Bliemer

Posts: 1588
Joined: Tue Mar 31, 2009 4:13 pm

### Re: Minimum number of choice situations and SQ

Thanks a lot Michiel for your very quick responses. This is very clear and VERY helpful.
p.lecoent

Posts: 8
Joined: Tue May 10, 2022 1:59 am

### Re: Minimum number of choice situations and SQ

Dear Michiel,
In the meantime, there has been modifications of the levels and the SQ description.
The main modification is that the level 1 of attribute INF now describes only the SQ and is no longer a possibility in the other alternatives. Indeed level 1 could not be realistically combined with the other attribute levels.
- Is the design below accurate? The problem that I see is that now b6 could not be interpreted for the SQ preference since it is confounded with the reference level of attribute INF: level 2. Is there an alternative to avoid this problem?

Thanks

Design
;alts=alt1, alt2, sq
;rows=12
;block=2
;eff=(mnl,d)
;model:
U(alt1) = b1.dummy[0|0] * INF[3,4,2] ? INF : Water substitution level INF=1 None INF=2 25% INF=3 50% INF=4 100% (INF =1 only used in the SQ)
+ b2.dummy[0|0|0] * HEAT[2,3,4,1] ? HEAT : Heat island effect surface reduction HEAT=1 0% HEAT=20 % HEAT=3 40% HEAT=5 60%
+ b3.dummy * CAR[2,1] ? CAR Reduction of road and parking space CAR=1 No Reduction CAR=2 Reduction
+ b4.dummy[0|0|0] * DISTANCE[2,3,4,1] ? DISTANCE Distance of closest solution to home DISTANCE=1 No new green solution DISTANCE=2 In front of your house DISTANCE=3 100m DISTANCE=4 500m
+ b5 * BILL [10,20,30,40,50,60] ? Increase of the water bill in €
/
U(alt2) = b1*INF + b2*HEAT + b3*CAR + b4*DISTANCE + b5*BILL /
U(SQ) = b6 + b5*BILLsq
\$
p.lecoent

Posts: 8
Joined: Tue May 10, 2022 1:59 am

### Re: Minimum number of choice situations and SQ

You are correct that "level 1" will be absorbed in the SQ constant in that case. This is not a major issue, except that you cannot directly interpret the SQ constant as you indicate.

This is one of the articles that I have referred to in other posts, they propose a hybrid coding method to deal with the issue but I have no experience with it.

Cooper, B., Rose, J.M. and Crase, L. (2012) Does anybody like water restrictions? Some observations in Australian urban communities, Australian Journal of Agricultural and Resource Economics, 56(1), 61-51.

Michiel
Michiel Bliemer

Posts: 1588
Joined: Tue Mar 31, 2009 4:13 pm

### Re: Minimum number of choice situations and SQ

Thanks Michiel.
p.lecoent

Posts: 8
Joined: Tue May 10, 2022 1:59 am 