# How the attribute interaction is defined in utility estimation?

In layman's to define attribute interaction we need to specify the interacting attributes in the CBC/HB.

In the input '.CHO' we are not mentioning anything about the attribute interaction. So how the interacting parameters are being estimated?

Is it creating another attribute with unique levels of the interacting attributes? Suppose, Brand and Price have significant interaction and each have 6 levels, so there will be another attribute with 36 levels. This levels will be dependent on the levels of brand and price.

When the price is linear then how the terms are defined?

Thanks for the help in advance. Also wish you a very happy new year.

Hi Sanmit,

Regardless of interaction terms, the CBC/HB software recodes your design information into effects/dummy coding where each parameter is assigned a 1/0/-1 value, depending on the coding method selected. With main effects, your 6/6 design would have 5 parameters per attribute, for a total of 10 parameters. The omitted parameter is equal to 0 for dummy coding, and negative the sum of the other five parameters in effects coding.

When you add in the interaction effect between the two, we don't actually add in 36 additional parameters. Due to the coding we use, we can estimate the parameters as differences from the main effects, so your 36 combinations only actually result in 25 new parameters to estimate. These are coded using the same effects/dummy coding as main effects parameters, based on which combination of the two attributes was represented in that concept.

Linear coding converts the prices to zero-centered values as described in the CBC/HB help (from within the CBC/HB program, go to the settings for attribute coding and press "F1").
answered Jan 18, 2017 by Silver (9,245 points)
Hi Aaron,

Thanks a lot for the reply.

Just for clarification can you explain what does you mean by estimating the parameters as differences from the main effect?

It would be great if you can give some light on the method when price is linear. So if the price had 3 levels and there are 2 brands. The level values are are -0.5, 0, 0.5. How does the main effect of price and interaction effect is being estimated?