ApolloChoiceModelling forum

Hi Apollo Team,

I'm grateful for your support in managing this forum.

I've posted previously about my survey, but I am uploading this as I have a different question related to data processing.

I conducted a choice experiment-based survey regarding zero-emission truck choices, including battery electric trucks and hydrogen fuel cell electric trucks. A total of 54 freight companies participated. One of the important explanatory variables for specifying models is the annual revenue of the participating companies. In my survey questionnaire, this variable was presented with five options, and respondents were asked to select one: 1) <$10M, 2) $10-15M, 3) $15-30M, 4) >$30M, and 5) Decline to state (i.e., N/A). The issue is that 16% of respondents chose the "decline to state" option. How would you recommend handling these 'Not Available' data entries?

I have considered the following options, but would like to know which one might be recommended, what cautions should be exercised for each, or if there is a better way to handle this situation:

1. Treating the Annual Revenue variable as a categorical variable.
2. Assuming 'N/A' corresponds to an average annual revenue (e.g., $10-15M in my survey).
3. Excluding the observations with 'N/A' for the Annual Revenue variable (i.e., using 84% of the total observations).
4. Excluding the Annual Revenue variable from model specification.

Please let me know if I need to provide any additional information.

I'd greatly appreciate any guidance and insights you could share. Thank you very much!

Best regards,

YB

Hi

I would in your case recommend option 1. Even when I treat income as a continuous variable in my models, I do not exclude people with missing data, nor do I assign them to another category. Rather, I estimate a different parameter for them, which would be in line with your idea to treat it as categorical, where this will happen anyway

Stephane

Hi Stephane,

Thank you for sharing your insights. I believe I've understood your suggestion, and I've applied the approach you recommended. Specifically, I've incorporated this categorical variable into an interaction term with vehicle purchase costs. Could you please review what I've done and correct any errors?

The annual revenue (AR) variable in my dataset takes on one of the following values:

*annual_revenue == 1 (for AR <$10M)
*annual_revenue == 2 (for AR between $10M-15M)
*annual_revenue == 3 (for AR between $15M-30M)
*annual_revenue == 4 (for AR >$30M)
*annual_revenue == 5 (for the case of declining to state)

I've treated 'AR > $30M' as the reference category and applied shift terms, as shown below:

b_pcost_value = b_pcost + b_pcost_AR_less_than_10M*(annual_revenue==1) + b_pcost_AR_between_10M_15M*(annual_revenue==2) + b_pcost_AR_between_15M_30M*(annual_revenue==3) + b_pcost_AR_NA*(annual_revenue==5)

An example of the utility function for one alternative (battery electric vehicle) is shown below:

V[["bev"]] = asc_bev_value + b_pcost_value * bev_pcost + b_ocost_value * bev_ocost + b_range * bev_range + b_offsite_value * bev_offsite_binary + b_onsite_bev * bev_onsite

With these settings, I've obtained the following estimation results: Only "b_pcost_AR_between_15M_30M" is significant at the 5% level.
I'm curious if there are alternative approaches for formulating the interaction term between this categorical variable and vehicle purchase costs. Also, I'm wondering if it's still meaningful to have obtained such a small number of significant estimates.

I'd greatly appreciate any suggestions or insights you could provide. Thank you very much!

Best regards,

YB

Hi

your specification is correct but your results are worrying as the effect in the reference group is positive and as the income effect is not monotonic

Stephane

Hi Stephane,

Thank you for sharing your insights. In my dataset, there are 54 respondents, and here is the distribution of their annual revenue (AR): The majority fall into the category of <$10M (56%). Only around 10% are dispersed among each of the remaining categories, and the number of respondents in each of these categories are relatively small (less than 10). Might this have contributed to the positive effect in the reference category and lack of monotonicity?

As an alternative approach, I simplified the specification as follows:

b_pcost_value = b_pcost*(AR_NA==0) + b_pcost_AR_NA*(AR_NA==1)

Using this, I obtained a negative value for the 'b_pcost' estimate, significant at the 10% level (t-ratio) or the 5% level (Robust t-ratio): Then, could this be a better approach? Any suggestions you have would be greatly appreciated.

Thank you!

YB

Hi

given your small sample size, this is a good approach

Stephane

Thank you Stephen,

I greatly appreciate you sharing your insight on the issues in this post and another one as well. I will get back to you if I have further questions. Once again, thank you for organizing this forum, which is very helpful for making effective progress on my research!

YB