Efficient designs

[Yashin Ali]

Dear Sir,

Does attribute level balance is necessary for D-efficient design ? I have 6 attributes with varied levels in each of the attribute. Hence, the attribute level is unbalanced.

[Michiel Bliemer]

No, attribute level balance is not necessary.

Note that your definition of attribute level balance may not be correct, a design can be attribute level balanced even if attributes have different numbers of levels.

For example, consider three attributes:
- attribute 1 has 2 levels
- attribute 2 has 3 levels
- attribute 3 has 4 levels

Then using a design with 12 rows (or 24, or 36, ...) can have attribute level balance. Namely, the levels of attribute 1 can each appear exactly 6 times, the levels of attribute 2 can each appear exactly 4 times, and the levels of attribute 3 can each appear exactly 3 times.

Michiel

[Yashin Ali]

Thanks, Professor. Here, I would like to add some information as well.

What happens if i want to restrict the rows = not more than 6tasks ? Moreover, the range of the attribute level in some cases are in equidistant spacing and in some attributes levels, are not equidistant (there exists a big difference in levels).
Creating a D-efficient design in this case isn't challenging or possible?

Any suggestions are highly appreciated. Here is the following Ngene code:

design
;alts = Tariff1, Tariff2, Tariff3
; rows = 12
;eff= (mnl,d)
;block = 2
;model:

U(Tariff1)=bchargingpower*Chargingpower[11,50,150]+bdist*Distance[500,1000,2000]+bcost*Price[40,60,90]+brwt*RWT[0,10,20]+bchargingtime*Chargingtime[90,105,420]/
U(Tariff2) = bchargingpower*Chargingpower +bdist*Distance +bcost*Price +brwt*RWT +bchargingtime*Chargingtime /
U(Tariff3) = bchargingpower*Chargingpower +bdist*Distance +bcost*Price +brwt*RWT +bchargingtime*Chargingtime
$

[Michiel Bliemer]

Levels can be equidistant or non-equidistant, this does not matter.
Using 12 rows and blocking it in 2 is fine.

Efficient designs are very flexible (unlike orthogonal designs) so what you are asking for is definitely possible and not challenging at all.

To avoid dominant alternatives in your choice tasks, I would recommend using near-zero priors that indicate the expected sign of each parameter (or leave 0 if you do not know), as in the syntax below, where I added also an asterisk after each alternative name. Note that I guessed the sign of the parameters, they may be wrong since I do not know the meaning of the attributes, so you will have to put in appropriate signs.

Code: Select all

design
;alts = Tariff1*, Tariff2*, Tariff3*
;rows = 12
;eff= (mnl,d)
;block = 2
;model:
U(Tariff1) = bchargingpower[0.000001] * Chargingpower[11,50,150]
           + bdist[ 0.000001]         * Distance[500,1000,2000]
           + bcost[-0.000001]         * Price[40,60,90]
           + brwt[-0.000001]          * RWT[0,10,20]
           + bchargingtime[-0.000001] * Chargingtime[90,105,420]
           /
U(Tariff2) = bchargingpower*Chargingpower +bdist*Distance +bcost*Price +brwt*RWT +bchargingtime*Chargingtime /
U(Tariff3) = bchargingpower*Chargingpower +bdist*Distance +bcost*Price +brwt*RWT +bchargingtime*Chargingtime
$

Michiel

[Yashin Ali]

Thank you sir!