Estimation of coefficients labeld choice experiment

[Michael_D]

Hello,

I have designed a labelled choice experiment with three alternatives. Lets say the alternatives are Apples, Ananas and Bananas. An attribute is price. Now the price varies between all choice sets in all alternatives.

For example choice set 1:
Apples 1 €
Ananas 1.5 €
Bananas 0.5 €

choice set 2:
Apples 1.5 €
Ananas 1.5 €
Bananas 1.0 €

Maybe my question is stupid but I asked myself whether I estimate a price coefficient for all three alternatives or only for two of them and one is the base?

Thank you for your help. Best regards
Michael

[Michiel Bliemer]

One would often estimate a single price coefficient assuming price as a numerical attribute, whereby the prices for different fruits can be different:

U(apples) = ... + b_price * price_apples[0.5,1.0,1.5] + ... /
U(ananas) = ... + b_price * price_ananas[1.5,2.0,2.5] + .../
U(bananas) = ... + b_price * price_bananas[1.0,1.5,2.0] + ...


But it is possible to estimate alternative-specific coefficients, here you would estimate 3 coefficients:

U(apples) = ... + b_apple * price_apples[0.5,1.0,1.5] + ... /
U(ananas) = ... + b_ananas * price_ananas[1.5,2.0,2.5] + .../
U(bananas) = ... + b_bananas * price_bananas[1.0,1.5,2.0] + ...


You could also treat price as a categorical variable and estimate two coefficients for two dummy variables, assuming the last level is the base level. This requires that all price attributes have the same levels:

U(apples) = ... + b_price.dummy[0|0] * price[0.5,1.0,1.5] + ... /
U(ananas) = ... + b_price.dummy * price + .../
U(bananas) = ... + b_price.dummy * price + ...


Alternatively, you could consider alternative-specific dummies and estimate 6 coefficients:

U(apples) = ... + b_apple.dummy[0|0] * price_apples[0.5,1.0,1.5] + ... /
U(ananas) = ... + b_ananas.dummy[0|0] * price_ananas[1.5,2.0,2.5] + .../
U(bananas) = ... + b_bananas.dummy[0|0] * price_bananas[1.0,1.5,2.0] + ...


Michiel