I have done a study with 575 sample size with two attributes. For one attribute, there are more than 100 levels and the other attribute is price which has 5 levels. The suggested prior degrees of freedom are 10 and the prior variance is 1.2.

I have also tried to estimate utility with increasing the prior variance ("Increasing the prior variance tends to place more weight on fitting each individual's data and places less emphasis on "borrowing" information from the population parameters") to 10 where I am getting a better hit rate and closer market alignment to share with compare to the suggested one.

In both the cases I have estimated utility with the assumption that price is linear and it has an interaction with the other attribute.

But the price sensitivity of the model with compare to the suggested one is going up. If we go with the suggested one the share of a major brand in the market is going down from 6.8 to 6.0. On other the utility with prior variance of 10 the share of the same brand is going down from 7.2 to 5.0.

Can someone throw some light on this phenomenon?

Thanks for the help in advance.

Thanks a lot for the prompt response.

We are estimating the raw hit rate by true/false per observation and there are 3 holdout task.

I got your point that, with increase in prior variance means larger utilities and bigger differences between best and worst utilities within an attribute.

Kindly help me with the following questions:

1) Is there any way we can derive an optimal prior variance for a particular study with two attributes and one of them will have more than 100 levels?

2) Increase in prior variance actually helps to improve the precision of the attribute with higher number of levels, as it create bigger differences between best and worst utilities within an attribute, but for price as an attribute, where the level will be maximum 5 or 6, the same might not be true. Is there any way we can creates bigger differences between best and worst utilities of those attributes which higher levels without impacting the price utility?

Thanks for the help in advance.