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HB: Confidence intervals of attribute coefficients

Dear Forum,

I have some trouble calculating the significance of attributes and levels as described in the book "Becoming an expert in conjoint analysis".

Understanding the alpha file:
In the file "Alpha-Convergence" I find columns named after the attribute levels (under the headline "Intercepts"). Moreover, there are columns with the attribute levels (under the headline "gender (1)" and "education (1-4)". (1) Why are there values for gender and education?
(2) After 20.000 iterations the draws still jump from Alpha < 1 to Alpha >  15.000.000 and back to Alpha < 1, how is that possible?
(3) How do I connect the alpha draws to the values in the utility report?

Calculating confidence intervals:
First, I would like to show that the none utility is a positive value, thus needs to be compensated with greater product utility (product utility - none utility = net utility) to elicit purchasing behavior. If 7 out of 20.000 alpha draws are negative, I can be 99,965% confident that the none utility is in fact positive, right?

Thank you very much for the support!

asked Jul 1, 2019 by Chris Berlin Bronze (570 points)

1 Answer

0 votes
Let's first describe the layout of the parameters in the alpha file.  Recall that when we add categorical covariates to the model, we are dummy-coding those covariates in the design matrix.  Let's consider Gender, where 1=Female and 2=Male.  Per the CBC/HB documentation, it tells us that we apply the covariate as a dummy-coded variable multiplied by the vector of part-worths, where the last code of the categorical covariate variable is the reference level (the 0 utility).

So, if we applied just Gender as a covariate, we would find two full sets of utilities in the alpha file.  First, we find the utilities associated with the intercept (the Male utilities, because the Male category was the final category as is the reference utility).  After the intercept utilities, we find the adjustments to the intercept utilities when respondents are Female.  So, the total female utility for the None parameter is equal to the intercept utility for None plus the Female adjustment to the Male utility of None.  (The two "none" parameters summed).

Please be careful in interpreting the None from ACBC, as it is not really the same idea of the None as from a standard CBC question.  The None utility in ACBC (assuming you just used default ACBC setup without the calibration purchase likelihood questions) is just the utility associated with the "not a possibility" choice from the screener section.  Asking respondents if each concept is "a possibility" isn't exactly the same question as asking respondents if they would buy a product concept or not.

The None utility (the "not a possibility" utility) is scaled with respect to the other parameters in the study.  And, effects coding leads to zero-centering of the utility parameters for the other attributes.  But, if you used "summed pricing" and have used "piecewise" coding for the continuous price variable, then price utilities are not necessarily zero-centered--and then the None utility needs to shift to compensate.  

I would be careful about the interpretation of the None utility from an ACBC study, where the None results from the "not a possibility" choice in the Screener section.  And, it's probably easier and more faithful to interpret the None utility by conducting market simulations where one product concept is compared to the None alternative.  Interpreting the raw None utilities can be problematic, especially if you have used piecewise coding for summed price.
answered Jul 1, 2019 by Bryan Orme Platinum Sawtooth Software, Inc. (201,565 points)