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### Continuous variable with uneven distance between levels

Posted: Tue May 14, 2024 11:59 pm
Hi there,

I have a variable with 3 levels (15,45,90). Is it okay to enter it in the DCE design as a continuous variable even though there are uneven distances between the levels? I’m trying to work out how I would interpret the results if I find a significant effect.

### Re: Continuous variable with uneven distance between levels

Posted: Wed May 15, 2024 2:27 pm
Yes that is fine, attribute levels do not need to be equidistant. In revealed preference data it is unlikely that observed levels are equidistant, so there is also no need for them to be evenly spread in stated preference data. Of course, some degree of evenly spread attribute levels is often desirable to be able to interpolate in forecasting. So if your levels are mostly around 90 and not many around 15 then your forecast of choice probabilities will be more accurate around 90 than 15. But for estimating a single coefficient for this numerical attribute you can use any levels you like.

Michiel

### Re: Continuous variable with uneven distance between levels

Posted: Thu May 16, 2024 5:55 pm
Thanks very much Michiel.

I have checked my design to ensure there is level balance for this variable.

I am running a pilot first as I do not have predictions for my other variables. For this continuous variable, I am assuming a negative effect of longer travel time on selection of the choice - so I am using a small negative prior b3[-0.00001]*traveltime[15,45,90]
Is this correct way sign for prior given the level order?

Have I understood correctly that I will be able to use the coefficient for the travel time variable in the model to calculate the value for each level - for example if I want to compare 90 vs 15?

### Re: Continuous variable with uneven distance between levels

Posted: Fri May 17, 2024 9:30 am
Yes that is the correct syntax. Although when using priors to generate an efficient design, I generally use dummy coding for all parameters, even for numerical attributes, to ensure that not only outer and inner levels are compared across alternatives (since this is most efficient when using zero priors). So in that case the syntax would become:

b3.dummy[-0.001|-0.002] * traveltime[45,90,15] ? where the last level is the base level

Using a single coefficient b3 * traveltime, the contribution to utility for level 15 is b3*15, while the contribution to utility for level 90 is b3*90. Using dummy coding the contributions to utility would become 0 for level 15 and equal to the second dummy coefficient for level 90.

Michiel

### Re: Continuous variable with uneven distance between levels

Posted: Mon May 20, 2024 9:00 pm
Hi Michiel,

Thank you for this.

Is dummy coding the continuous variable essential?

I have checked that there is level balance for the continuous variable (perfect balance across the design, near perfect balance within blocks), does this resolve the issue of inner and outer level comparisons?

My concern is that dummy coding, the variable will add another parameter and change the design. For context, I have already developed my design based on the number of parameters to estimate (12, including a constant), – and all my attributes have three or four levels – so I have created an efficient design with 36 three sets of blocked into 3.

### Re: Continuous variable with uneven distance between levels

Posted: Tue May 21, 2024 9:15 am
Check your design to see if across two alternatives you mainly see trade-offs between 15 and 90 minutes, and trade-offs between 45 and 45 minutes. You also may want to check other numerical attributes. This often happens when using zero priors for numerical attributes. If this does not happen in your case then you are fine. If it does happen, then there are only two ways to resolve the issue: (i) using dummy or effects coding when generating a design with zero priors, or (ii) using an orthogonal design. Your design size of 36 rows should be sufficient to do this as in the end you will only estimate 12 parameters, so I would not worry that much about using dummy coding during the design phase, even if this increases the number of parameters in the "design model". I think it is more important to avoid trade-offs only between outer and inner levels. But again, if this issue does not arise then you are fine.

Michiel

### Re: Continuous variable with uneven distance between levels

Posted: Sat May 25, 2024 4:50 pm
Hi Michiel,

Thank you very much for this! I should have mentioned that it’s a binary choice design - participants will see single choices and answer Yes/No. there is level balance across and largely within blocks so hopefully that will be okay in this case.