details of RFC

Question

I have to mimic RFC simulation in our proprietary simulation software.
I have read both the documentation and Huber, Orme, Miller 1999 article on simulations with RFC. Yet I'm still missing some parts of the algorithm.

1. What distribution does the attribute error follows?
2. What are the values of Gumbel parameters for product error? mi = 0, b = variability (from simulation setting).
3. Where the exponent is used. As I understand RFC does multiple randomized (by errors added) first choices. So there is no evident place where exponentiation is done.

Answer 1

1.  With the SMRT software implementation of RFC, we use Gumbel error.  However, after further reflection (and realizing that adding multiple Gumble errors across attributes tends toward normality) we decided to use normal error for the Online Simulator implementation of RFC.

2.  Product error by default uses zero * Gumbel error.  If the user adds any product-type error, this makes the results more influenced by IIA.

3.  The exponent (scale multiplier) is applied prior to perturbing the utilities by the attribute and product type errors.

Comments

Thank you Bryan!
Concerning my second question I was curious what are parameters of this Gumbel distribution.  As Gumbel has two parameters mi and beta I need them to simulate the error term. I suppose this gumbel error should be zero centred. The  dispersion parameter isn't of much practical concern as it changes only the scale of the error and we adjust scale by multiplier. But to check my results with SMRT I should know the beta used in SMRT. If not the beta maybe the standard deviation of your gumbel as they are strictly linked.