We have a pricing CBC study with constructed price (hidden price levels with 3 other attributes that would give total price: TotalPrice=HiddenPrice x Attribute1 x Attribute 2 x Attribute 3).

Research Question #1:

Do respondents really try de-construct the price to the hidden price levels in their mind when thinking about the total price and making decisions?

Trying to answer that, we've run HB estimations for main effects only and for all possible variants of interactions between hidden price and attributes that are bundled with it in constructed price.

The results show that interactions are in evidence. Fit scores for interactions are 10-20% higher than for main effect only. Based on that, my initial reaction was - Yes! People didn't get much deeper than the total price they saw on the screen. Therefore they don't preform any calculations.

On the second hand, I feel respondent still try to do these calculations as the fit scores for main effect only are not bad and the importance of hidden price attribute is the second highest in the "main effect only" model.

So there could be a mix of approaches on how people think about price.

1.1) Is there way to quantify these proprtions of effects

1.2) Is it a correct approach to use 3 2-way interaction effect in the same run, whereas the total price were affected by 3 attributes simultaneously?

1.3) Given that we see lots of interactions there, how can we estimate the real importance of total price as opposed to importance of hidden price attribute?

Research Question #2:

If respondents do not de-construct the total price or they do de-codnstruct it only partially - what would be the pathway or sequence of attempts? Would they try to divide the total price, for instace, by Attribute2 first then by Attribute 1 then by Attribute3?

To answers that we checked how single pair Attribute x HiddenPrice interaction effect performed. Which specific single pair of interactions had lowest contribution to the model. The lowest contribution one would mean respondents did some calculations for that specific pair and therefore get closer to the main effect for HiddenPrice.

2.1) is it a correct interpretation?

2.2) Are interaction effects affected by the number of levels? If Attribute1 has 4 levels and Attribute2 6, would it be fair to compare interaction effects of each with price and make the above conclusions?

If not comparable, how to adjust it?

...and generally is there a significance measure of iteractions? Which iteraction effect is considered weak and be ignored?

Thanks