Have an idea?

Visit Sawtooth Software Feedback to share your ideas on how we can improve our products.

What is the mathematical relationship between aggregate logit and HB estimates?


This may be a very daft question and show my ignorance of bayesian statistics, however, what is the mathematical relationship between the aggregate estimate of a parameter (in this case a linear term) and the average of the individual HB estimates from a group of respondents. I ask because clearly the scale of the HB estimate is larger in magnitude than the logit estimate, yet they are almost perfectly correlated. Is there a way to workout the inflation factor?

The reason I ask is that I need to generate estimates in the magnitude of a a nested logit model for further use in a strategic transport model, but I want to take advantage of the clear benefits of using HB estimation. However, the average of individual HB parameters is to large for use in the model, so I need an equivalence with Logit parameters. Is there a clear mathematical between the terms such that I can reduce the HB estimate to the same scale as the Logit estimate?

Many thanks in advance.
asked Jul 19, 2018 by Jasha Bowe Bronze (1,745 points)

1 Answer

0 votes
Both aggregate logit and HB are based on the MNL model.  But, HB is a quite different animal, involving a balancing act between the lower-level fit (likelihood of fitting the individual-level choices) and upper-level fit (likelihood that the individual respondents seem to be drawn from the multivariate distribution of the upper-level estimates).  Furthermore, the scaling of HB parameters is affected by the prior settings (prior variances especially).

I have also found that HB leads to mean population estimates that are highly correlated with aggregate logit estimates, but with a shift in their scaling.  There is not a simple adjustment factor, such as HB population estimates are 1.5x the scale of aggregate logit estimates.
answered Jul 19, 2018 by Bryan Orme Platinum Sawtooth Software, Inc. (160,485 points)