ACBC HB estimation of the None utility

Question

Dear forum,

I´d be very grateful for a clarification about the estimation of the None Utility within ACBC designs and HB estimation.

In the ACBC´s technical guide it says:
"Each respondent has marked T concepts as "possibility" or "not a possibility." We treat these each as binary choices, where the respondent is assumed to compare the utility of the concept to the utility of a constant threshold prior to making a choice. The constant threshold is included in the design matrix as an additional dummy coded column."

I don´t get the last bit.
Is the none utility part of the iterative estimation procedure (MCMC) drawing on the choice tournament data or fixed after the screening section?
Does "design matrix" refer to the variance-covariance matrix D respectively is the none utility one element of the vector β (part worth utilities) or is it something completely different?

Thank you very much for your support!

Best,
Chris

Answer 1

The none utility (the "not a possibility" category from the Screener section) is estimated as a part-worth utility parameter during the utility estimation.  

We stack the three sections of the ACBC data into one big regression matrix, with the BYO tasks, Screener tasks, and Choice Tournament tasks all being sections (series of rows) within that matrix.  The None parameter is a dummy-coded (independent variable) column in that regression matrix, and it only can take on values of 1 for the Screener rows of that matrix (when the alternative being coded is the "not a possibility" alternative); for the BYO and Choice Tournament rows, that dummy coded independent variable is always 0.

Design matrix refers to the coding of the independent variables for the rows (cases) shown to the respondent, often referred to as the X matrix.