Interaction terms with orthogonality and optimal design

[zshroff]

Thanks for your suggestions, I am now looking at using an efficient design as an alternative. For each of my attributes , I do know the expected sign ( ie which level would be preferred by a rational decision maker). If I had to implement it

a) how would the design below fare ( after adding information on the sign of priors, question on that below) ? I would really appreciate your comments on it since I have been studying OOD design all this while, I am looking to incorporate , at least the signs of the priors
b) should I keep the ;orth= seq command before the ; eff=(mnl,d) ? Will this create an efficient design and yet keep orthogonality? Also, in practice what is the impact of letting orth, default to simultaneous versus adding the sequential command ?
c) how do I incorporate priors, only knowing the sign for attributes that are common across alternative choices( all my attributes are common across alternatives)- ie should I use just a minimal number to indicate the sign [0.5]
d) should I use the same number in the prioirs for all the attributes since I don't know anything beyond the sign of the degree of preference. I ask this especially, since the number of levels in attributes may be different, or should I use a lower number value for attributes with more levels, to not give a higher value to these attributes ?
e) When I run this, I get a number of evaluation versions, while I understand that the algorithm is trying to minimize the d-error , is it ok to use one of the earlier( not last) desings taking into account dominance ( some of the designs with this algorithm still show dominant sets), d error, s estimates together, instead of just going with the last design produced

Design
;alts=alt1*, alt2*
;rows=24
;orth=seq
;eff = (mnl,d)
;model:
U (alt1)= b2*A[0,1,2,3] +b3*B[0,1] +b4*C [0,1] + b5*D[ 0,1] + b6*E[0,1,2,3] + b7*F[0,1] + b8*E*F /
U (alt2)= b2*A +b3*B +b4*C + b5*D + b6*E + b7*F + b8*E*F $

Thanks once again for your help,
Zubin

[Michiel Bliemer]

The syntax you wrote looks good, you indeed put stars behind the alternatives so Ngene knows they are generic and therefore Ngene can check for strictly dominant alternatives. Note that without priors, Ngene cannot determine which choice tasks may contain dominant alternatives. Preferably you will use parameter estimates from a pilot study, but if you know the sign and not the actual value, then enter value close to zero with the correct sign (so indeed 0.01 or -0.01). So it would be something like b2[0.01] * A[0,1,2,3]

You can keep the ;orth = seq command if you like, then at least you maintain orthogonality within each alternative (although it is not necessary).

It is important to note that the levels that you use for efficient designs need to be the actual levels that you will use in estimation. So if A was a cost variable, it could be 5, 10, 15, and 20 (dollars) instead of 0, 1, 2, and 3 (which is design coding that is typically only used when generating orthogonal design). So when you use the actual values of the levels, and you provide the prior (sign), then Ngene can compare each attribute between alternatives and see if one alternative has preferred levels for all attributes over the other alternative. By using real values, you assume indeed some kind of ordering, where 5 dollars is preferred over 10 dollars (with the associated parameter having a negative sign). So attribute A in your syntax is now assumed a continuous variable (like cost), but not a categorical variable (like comfort or colour). If you have categorical variables, then you have to enter them in the model as you would estimate the model, so for example b2.dummy[0.01|0.02|-0.01] * A[0,1,2,3], where 3 would be the base level for dummy coded variables, and the priors would be set in such a way that the ordering makes sense (if there is any ordering).

So when you have entered the priors, the dominant choice tasks should no longer occur, and you can take the last design that in the output screen with the lowest D-error.

So you are almost there

Michiel

[zshroff]

Thank you once again for your help in designing this choice experiment. My design examining health worker preferences for jobs in a developing country has six/seven dummy attributes coded as dummy variables [0,1] where 1 is the preferred option and one continuous variable (salary offered) [150, 300, 450, 600]. I have incorporated your feedback and want to confirm that I have understood correctly.

(a)Please see the syntax if this is how it should read if I want Ngene to read level 1 as higher utility then level 0 (from your example in the last reply , I gathered that Ngene uses the last level as the reference group in coding dummy variables)

Design
;alts=alt1*, alt2*
;rows=24
;orth=seq
;eff = (mnl,d)
;model:
U (alt1)= b2.dummy[0.01]*A[1,0] +b3.dummy[0.01]*B[1,0] +b4.dummy[0.01]*C [1,0] + b5[0.01].dummy*D[1, 0] + b6[0.01]*E[150,300,450,600] + b7.dummy[0.01]*F[1,0] + b8.dummy[0.01]*G[1,0]+b9.dummy[0.01]*H[1,0] /
U (alt2)= b2*A +b3*B +b4*C + b5*D + b6*E + b7*F + b8*G + b9*H $

b) In putting priors for the continuous versus dummy variables, is using the same prior for the dummy and the continuous variable the right thing to do , since the utility in the continuous variable is being multiplied taking into account 150 and 600, or should I stick to the same value of the prior for all the variables( this gives me very strange S estimates). In other words, should I attempt to make the utilities for the upper levels equal . ie in the example above if b6 has utility[0.001], then b2 should have 0.6 (0.001*600). Else I feel I am comparing 0.001 with 0.01*600=0.6 when comparing dummies with the continuous variable.


c) I am still getting dominant sets(in that some attributes, levels are equal across alternatives but in attributes that are not, all the levels in one choice set are ‘superior’ ie, those that would be chosen by a rational decision maker, making the choice set appear quite redundant) Why is Ngene not able to remove these sets ? Is there any way I can resolve this, using priors or conditions for instance? However, in some choice sets , making one of the dummy attributes a three level attribute appears to address the dominance issue.



d) Related to this, when I use the same priors for all the attributes ( running the model above) the S estimate is huge, in the tens of thousands ? When I use a much smaller parameter in front of the continuous variable for example 0.001 versus 0.6 in front of the dummy ( since the maximum value of the continuous variable is 600 times the dummy), I get much more reasonable estimates. How does this matter in terms of sample size? I am looking at 24 choice sets for 100 respondents for each of the groups I will be interviewing

Thank you once again, I hope to finalize my choice sets in the next day or so.
Zubin