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Dear Michiel,

Hope everything goes well for you.

I am trying to build a labelled design. There are 6 alternatives with two attributes: price (p) and tax (t). For each attribute, I will have different levels in each alternatives. Can I make same coefficients (b0 for price, b10 for tax) of price and tax for all utility functions? Or I have to use different coefficients for each utility function?
Thanks.

Wei

Code: Select all

Design
;alts = conv, gras, plan,lab, org.gras, nobuy
;rows = 8
;orth = sim
;block = 2
;model:
U(conv) = b1 + b0 * p1[3.64, 4.42, 5.20, 5.98] + b10 * t1[0, 0.05, 0.09, 0.14]/
U(gras) = b2 + b0 * p2[4.46, 5.56, 6.66, 7.76] + b10 * t2[0, 0.09, 0.17, 0.26]/
U(plan) = b3 + b0 * p3[7.49, 9.65, 11.81, 13.97] + b10 * t3[0, 0.01, 0.02, 0.03]/
U(lab) = b4 + b0 * p4[10, 23.33, 36.66, 49.99] + b10 * t4[0, 0.02, 0.04, 0.06]/
U(org.gras) = b6 + b0 * p6[5.44, 6.62, 7.8, 8.98] + b10 * t6[0, 0.06, 0.12, 0.18]

Hi,

Apologies for the late reply, I was a week on leave.

You can do both. If you keep the coefficient generic across all labelled alternatives then you are saying that the sensitivity to price and tax is the same for all alternatives. However, there may be circumstances where these sensitivities may be different across labelled alternatives, in which case you may want to estimate alternative-specific coefficients. The latter would of course increase the number of parameters to estimate, and therefore would require a larger design (i.e., more choice tasks), but it would give you the opportunity to later test whether the coefficients are alternative-specific or generic, whereas if you assume that they are generic in generating a design you may not be able to estimate alternative-specific coefficients at a later stage. So it depends on the final model you expect to estimate.

Reasons for alternative-specific coefficients may for example be that for certain labels one may be more willing to pay more tax or a higher than for other labels. For example, if one of your labels is an environmentally friendly option then people may be less price/tax sensitive and therefore alternative-specific coefficients may be useful.

Michiel

Hi Michiel,

Thanks so much for your response. Could you share some methods to test whether the coefficients are alternative-specific or generic?

Thanks,

Wei

To test, you estimate a model with alternative-specific coefficiens, say beta_{j,k} for each attribute k and alternative j. Then you test the statistical hypothesis:

H0: beta_{j1,k} - beta{j2,k} = 0

where j1 and j2 are two different alternatives and you apply a t-test for which you need to compute the expected value of beta_{j1,k} - beta{j2,k}, which is straightforward, but you also need the variance of beta_{j1,k} - beta{j2,k}, which requires applying the Delta method using the variances of beta_{j1,k} and beta{j2,k} and the covariance between the two. You can find more information about the Delta method in the literature.

If you cannot reject the null hypothesis, then you may decide to use a generic coefficient across alternatives, beta_{k}.

Michiel

Thanks so much! They are really helpful.

Wei