Defining attribute as absolute and relative quantity

[claudiab]

Dear all,

I have generated a Bayesian efficient design including 5 attributes (each with levels) and using choice tasks with two product alternatives and a no-buy alternative.

Specifically, one attribute is the price the consumer is willing to pay for the product (price of the product), while one other attribute is the price, or amount of money, that is given to the producer (price paid to producer).

Now, let's take a choice task as an example where price of the product = $2, and the price paid to producer = $0.20.

I'd like to test whether the utility of my survey respondents is more affected by the absolute amount paid to the producer = 0.20$ or by the share paid to the producer (price to producer / price of the product for each alternative), that is in this case the 10% (0.10 = $0.20 / $2).

To perform such a test, I'm thinking to split the sample into two subsamples. With the first half of the sample, I would implement the Bayesian efficient design I've already generated by using the absolute amounts of the price paid to the producer ($0.20 in my example). With the second half of the sample I would use a design describing the “share paid to producer” ($0.10 in my example) instead of the absolute amounts of the price paid to producers. I am wondering which design approach would be more suitable for the specification of the share paid to producer attribute. Specifically, I am debating whether to use one of the following two options:

Option 1: Implement the same efficient design I have already generated where I simply replace the attribute "price paid to producer" with the "share paid to producer"; in other words in the choice task of my example I simply replace $0.20 with 10% and keep all the remaining attributes and levels the same as in the Bayesian design I've already generated. With this approach, however, I observed that the “share paid to producer” attribute would have a different number of levels in comparison with the original “price paid to producer” attribute.

Option 2: Generate a completely new efficient design where instead of the price paid to producer I use the new attribute share paid to producer which can have four levels, for example. This option generates a new design with choice tasks different from those presented in the first half of the sample.

In your opinion, should I go for option 1 or option 2? Or in case you have further suggestions, they are definitively more than welcome.

Thanks in advance for your kind attention and support.

Claudia

[Michiel Bliemer]

Hi Claudia,

Two things:

1. It probably does not matter a lot whether you create a completely new design or not, the efficiency of the design will be similar. If you would like to have a different number of levels, there is nothing wrong with generating a separate design with the relative amount.

2. In the comparison, there is no need to keep the design the same, but I would highly recommend you to keep the sample the same. The reason is that if you find differences between sample 1 that see absolute prices and sample 2 that sees relative prices, you cannot conclude that this is due to absolute or relative prices because it could be because your two samples are different. Therefore, it is best to give choice tasks with both absolute and relative prices to the same respondent. For example, if you create two designs with 8 choice tasks, you create two versions in which respondent 1 faces the first 4 choice tasks of each design, and respondent 2 faces the second choice tasks of each design (and you probably would like to alternate the order in which they see absolute or relative prices). Because the sample is now the same for both designs, any differences in behaviour observed can be attributed to a difference in absolute or relative price. In your model estimation, you may want to correct for scale differences in the two designs (by estimating a heteroscedastic model), but if you use a design that is very similar for absolute/relative prices then you can likely ignore the scale effect.

Michiel

[claudiab]

Dear Michiel,
Sorry for my late response, but I wanted to check base with my co-authors that we understood the process you suggest correctly.
Basically, let’s pretend I have a design with three blocks and each block consisting of four choice tasks. In this design, I use the absolute price. I generate a similar design, i.e. three blocks and each block consisting of four choice tasks, specifying the price as relative value. For each block, I will propose to one respondent two tasks from the “absolute price design” and two tasks from the “relative price design”, while I will present to another respondent the remaining two choice tasks from the two respective designs.
Then, when I analyze the data, I will specify the variable as the absolute price in case of both designs, but correcting for scale differences using a heteroscedastic model, unless I use a design that is very similar for absolute/relative prices.
Is this correct?
If yes, I have tried several combinations to check for a design very similar for absolute/relative prices, which is actually what I would like to obtain, but unfortunately without success. The only “trick” that worked out was replacing the absolute values with the relative values from the original absolute price design. However, I used the “eval” command and noticed that the efficiency of the design is way worse.
Anyway, I thank you very very much for your kind suggestion. I really appreciate it.
Claudia

[Michiel Bliemer]

1. Yes that is correct.

2. When you convert the absolute differences into relative differences, you also change the priors, correct? The attributes will have a different unit and the parameters will have a different unit as a result. Because unit differences also the D-error will be different. You cannot compare the D-error when the attributes and units are different, so I am not sure you can say that the efficiency is "worse". You can try to optimise the design for relative prices and see if the optimal design has a much better D-error. I suspect it will not be very different.

Michiel

[claudiab]

Michiel,

ok, I will do so!
Thank you so much.

Claudia