Calculating attribute combinations excluded by constraints

[mquaife]

Hi all,

Thank you for developing such useful software and for maintaining this useful support network

I would like to respond to a comment on a paper where I have used a d-efficient design with constraints of how frequently a product can be used. A reviewer has asked us to calculate the number of potential attributes excluded due to these constraints, and despite lots of reading around I am struggling to calculate this by hand.

Could you suggest a method to do so? Or, even better, if this is shown in NGENE somewhere?

Thanks
Matt

Syntax as below (unlabelled design):

Design
;alts=A,B,C,none
;rows=10
;eff=(MNL,d)
;cond:
if(A.product= 1, A.freq = [0,2,3]),
if(B.product= 1, B.freq = [0,2,3]),
if(C.product= 1, C.freq = [0,2,3]),
if(A.product= 2, A.freq = [1]),
if(B.product= 2, B.freq = [1]),
if(C.product= 2, C.freq = [1]),
if(A.product= 3, A.freq = [0,1]),
if(B.product= 3, B.freq = [0,1]),
if(C.product= 3, C.freq = [0,1]),
if(A.product= 4, A.freq = [2,3,4,5]),
if(B.product= 4, B.freq = [2,3,4,5]),
if(C.product= 4, C.freq = [2,3,4,5]),
if(A.product= 5, A.freq = [4,5,6]),
if(B.product= 5, B.freq = [4,5,6]),
if(C.product= 5, C.freq = [4,5,6])

;model:
U(A)=
Att1.effects*Att1[1,2,3,4,5]+
Att2.effects*Att2[1,2,3]+
Att3.effects*Att3[0,1] +
freq.effect**freq[0,1,2,3,4,5,6]+
Att5.effects*Att5[0,1]+
Att6.effects*Att6[0,1,2,3]/

U(B)= as above
U(C)= as above
U(none)=b1
$

[Michiel Bliemer]

i assume that the question is how many choice tasks (out of the full factorial) are excluded? there are no attributes excluded, all attributes appear in the design.

You can do this without Ngene.

The total number of choice tasks can be calculated as:
(# of profiles available for alt A) * (# of profiles available for alt B) 8 (# of profiles available for alt C)

Since the numbers for alts A, B, and C are the same, you can just calculate for alt A.

The full factorial for alt A is 5*3*2*7*2*4 = 1680
So the full factorial over all alternatves is 1680^3 = 4,741,632,000

The restricted number of profiles due to contraints for alt A is:
1*3*3*2*2*4 +
1*1*3*2*2*4 +
1*2*3*2*2*4 +
1*4*3*2*2*4 +
1*3*3*2*2*4
= 624
So the total number for all alternatives is 624^3 = 242,970,624

Therefore, the constraints allow only 5.1% of the total number of possible choice tasks.

Is this what you are looking for?

Michiel

[mquaife]

Hi Michiel

Thank you very much - that is precisely what I was searching for. Appreciate your quick response despite study leave.

Matt