Level balance and correlation

[connie]

Dear Professors and experts:
I am new to DCE. I plan to design a DCE targeted to patients with specific disease. I have six attributes; all can be considered as continuous variables. The following are the attributes and levels:
Attribute A: [4,6,8,10,12]
Attribute B: [0,2,4,6,8]
Attribute C: [0,1,2,3,4]
Attribute D: [0,1,2,3,4]
Attribute E: [5,6,7,8,9]
Attribute F: [9,12,15,18,21] (price attribute)

The sum of the first five attributes should be less than a number. I used 'require' command. The following is my code:

Code: Select all

Design
;alts=alt1,alt2,none
;rows=12
;eff=(mnl,d)
;alg=mfederov
;require:
alt1.A+alt1.B+alt1.C+alt1.D+alt1.E=alt2.A+alt2.B+alt2.C+alt2.D+alt2.E,
alt1.A+alt1.B+alt1.C+alt1.D+alt1.E<=20,
alt2.A+alt2.B+alt2.C+alt2.D+alt2.E<=20
;model:
U(alt1)=b01[0]+
        b1[0]*A[4,6,8,10,12](1-4,1-4,1-4,1-4,1-4)+
        b2[0]*B[0,2,4,6,8]+
        b3[0]*C[0,1,2,3,4]+
        b4[0]*D[0,1,2,3,4]+
        b5[0]*E[5,6,7,8,9]+
        b6[0]*F[9,12,15,18,21](1-4,1-4,1-4,1-4,1-4)
/
U(alt2)=b02[0]+
        b1*A+
        b2*B+
        b3*C+
        b4*D+
        b5*E+
        b6*F
$

I have several questions:
1. I know it is impossible to have level balance in this case. But I hope the middle levels of each attribute appears more times than the two sides of the levels. For example, for attribute A, level 6,8 10 should appear more times than level 4 and 12. Based on my above code, level '0' in attribute B, C, D and E appear more than 12 times, which obviate from realistic scenario. If I set frequency of levels following each attribute, Ngene fails to find to optimal design due to too many constraints. I know there is 'soft' balance, using eff=(mnl,d)+0.5*(imbalance). But it seems not working. Any suggestions on this?
2. Following the point 1, if I set too many constraints, the correlation (Spearman Rank) will be high among attributes. This is because I set the sum of first five attributes less than a fixed number; a potential collinearity among attributes. I would like to know what is value of correlation is acceptable. In spearman rank, I saw two to three correlation coefficients are larger than 0.5. Are those too high?
3. I am struggling to balance point 1 and 2. I hope to have a design which close to real scenario and have low correlation among attributes. Any suggestions on my code?

Thank you so much!

Connie

[Michiel Bliemer]

1. I tried level constraints (1-2,1-6,1-6,1-6,1-2) and that seems to be working.

2. Correlations of 0.5 are fine. It usually becomes problematic with very high correlations, e.g. 0.95.

3. I hope that my above suggestions help out. Please let me know if you have further questions.

Michiel

[connie]

Thank you, Professor Michiel.
Please let me ask another two questions.
1. I am now thinking about generating a reference alternative, which is the sample average and the same for everyone. I followed Ngene book 8.3.2. The following is my code. However, Ngene crashes when I ran the following code.

Code: Select all

Design
;alts=alt1,alt2,none
;rows=12
;eff=(mnl,d)
;alg=mfederov
;require:
alt1.A+alt1.B+alt1.C+alt1.D+alt1.E=alt2.A+alt2.B+alt2.C+alt2.D+alt2.E,
alt1.A+alt1.B+alt1.C+alt1.D+alt1.E<=20,
alt2.A+alt2.B+alt2.C+alt2.D+alt2.E<=20
;model:
U(alt1)=b01[0]+
        b1[0]*A[4,6,8,10,12](1-4,1-4,1-4,1-4,1-4)+
        b2[0]*B[0,2,4,6,8]+
        b3[0]*C[0,1,2,3,4]+
        b4[0]*D[0,1,2,3,4]+
        b5[0]*E[5,6,7,8,9]+
        b6[0]*F[9,12,15,18,21](1-4,1-4,1-4,1-4,1-4)
/
U(alt2)=b02[0]+
        b1*A+
        b2*B+
        b3*C+
        b4*D+
        b5*E+
        b6*F
U(none)=b1*A1[8]+b2*B1[2]+b3*C1[2]+b4*D1[1]+b5*E1[7]+b6*F1[15]
$


2. Another question may sound stupid. For the opt-out choice, may I use the results of the design with opt-out, and replace opt-out choice with the reference alternative manually ? For example, some paper did not provide 'choose neither', but 'choose my current situation'. However, they did not mention using pivot or on-line panel. Moreover, 'current situation' varies by individuals. So I guess they may just input current alternative manually. Any suggestions on this if I want to compare hypothetical choices with their current choice?

[Michiel Bliemer]

1. When I run Ngene with this syntax it does not crash but rather generates an error message because you forgot to put a / after the second utility function. Adding a / resolves the issue.

2. Changing the opt-out to a status quo or reference alternative will affect the efficiency of the design. There is no real problem in doing it, you just lose efficiency. If the reference alternative is respondent-specific, then there are different strategies you can follow as outlined in Rose et al. (2008). One of them is that you use the average attribute levels to optimise the design, which you have done, and replace these average attribute levels with the respondent-specific levels reported prior to the choice experiment in the survey. You can also create a library of designs where you create multiple versions of survey and you take a specific design for each particular class of respondents. This increases the efficiency of your data collection since you optimise each design for each class, but it also makes your survey instrument more complicated.

Rose, J.M., M.C.J. Bliemer, D.A. Hensher, and A. Collins (2008) Designing Efficient Stated Choice Experiments in the Presence of Reference Alternatives. Transportation Research Part B, Vol. 42, pp. 395-406.

Michiel