I am currently looking into the following research paper:


However, I can not seem to understand two concepts that the author mentioned on page 3.

(1) In the equation $$U^I_{ijp}=X_{jp}\beta^I_{i}+\epsilon^I_{ijp}$$ I understand that $X_{jp}\beta^I_{i}$ provides the required linear combination, but what is the relevance of adding $\epsilon^I_{ijp}$ to it? (Is it the error term? Why do we need it?)

Moreover, it is mentioned that "$\epsilon^I_{ijp}$ follows an independent and identically distributed standard normal distribution that implies a multinomial probit model of choice". I definitely don't comprehend this part and need some help here.

(2) Another source of confusion for me is the line on the same page that reads "Consumer-specific attribute importance weights are allowed to vary across consumers, and to be correlated across attributes, as follows:"$$\beta^I_{ik}\sim N\big(\bar\beta,\Sigma\big)$$

This is the first time that I'm trying to study a research paper on my own, so excuse me if my question seems a bit trivial. Needless to say, I'd be grateful if someone could shed some light here (or redirect me to the right study material).


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