Two-step analysis

[erikadk]

Hi everyone,

I am looking for some advice on which model specification to use for the analysis of choice experiment data.
I have choice experiment data on fertilizer preferences. The design included two fertilizer alternatives as well as an opt-out alternative.
When one of the two fertilizer alternatives was chosen, the respondent was asked to indicate whether they would use that fertilizer as a complement (C) or as a substitute (S) to their current fertilizers.

I have previously used the Apollo package to estimate MNL (and MMNL) models to estimate fertilizer preferences. To do this, I used the following (simplified) utility functions:
V[["alt1"]] = b_price * price.1 + b_npk * npk.1
V[["alt2"]] = b_price * price.2 + b_npk * npk.2
V[["alt3"]] = asc
with the values 1,2,3 being the values of choice variable 'choice', corresponding to the respective alternatives.

Now, I'd like to know how the fertilizer attributes influence whether they are used as C or as S. I have tried to analyze this by creating a new variable called "use", equal to 1 when the fertilizer was chosen as a complement, 2 when the fertilizer was chosen as a substitute and 3 when the opt-out was chosen. Then, I estimated a similar MNL-model with the following utility functions:
V[["use1.1"]] = b_price_c * price.1 + b_npk_c * npk.1
V[["use1.2"]] = b_price_c * price.2 + b_npk_c * npk.2
V[["use2.1"]] = b_price_s * price.1 + b_npk_s * npk.1
V[["use2.2"]] = b_price_s * price.2 + b_npk_s * npk.2
V[["use3"]] = asc
with the values 1.1, 1.2, 2.1, 2.2 and 3 being the values of the new choice variable 'use', corresponding to the respective use options: 1.1 if alternative 1 was chosen as a complement, 1.2 if alternative 2 was chosen as a complement, 2.1 if alternative 1 was chosen as a substitute, 2.2 if alternative 2 was chosen as a substitute and 3 if the opt-out was chosen.

I am wondering if this is the correct approach, or if I need some kind of 2-step procedure.
Any help is greatly appreciated!

Best,
Erika

[stephanehess]

Erika

so the second question is only asked if they choose one of the fertiliser options. In that case, you would need to only use those rows of the data where that happens (you can use the rows setting for that). Also, your current code assumes that both fertilisers are available in that second choice, but I understand it is only for the chosen one. So you would also need to set availabilities, e.g.

avail=list(use1.1=(choice_stage1==1),
...)

[erikadk]

Thanks a lot for your response, I really appreciate the help.

If I understand correctly, the idea is (1) to only use the rows where respondents chose one of the two fertilizer alternatives (excluding those who selected the opt-out), and (2) to only account for the attributes of the fertilizer they selected in the first stage of the experiment. This makes sense, as we are narrowing the analysis to just the chosen alternative.

However, by focusing on just the chosen fertilizer and excluding the alternative, there is no trade-off between the attributes anymore.
Would it then be valid to use a simple binary logit model, where the comparison is only between using the chosen fertilizer as a complement or a substitute?

Looking forward to your thoughts!

[stephanehess]

Hi

well, if the question they are being asked is for the chosen alternative only, then there would be no trade-off. But of course the attributes of the chosen alternative would still influence the choice between C and S.

Does that make sense?

Stephane