Do you mean that when you used the simulated choices to estimate part-worth utilities using logit or HB analysis, the part-worth utilities failed to reflect very closely your initial user-defined coefficients?

I'll assume that was the issue. Please correct me if not.

For simulating data in CBC with known respondent utilities to see if they may be recovered using utility estimation (a common thing to do!), here are some thoughts:

For aggregate logit, you should assume each respondent has the same \"true\" utilities (without any variation), and the only variability is in the response error. You add the true utilities (identical for each respondent, where the utilities are zero-centered within each attribute) for the given choice task, but prior to having the robotic respondent choose the alternative within the set with the highest utility, you first add Gumbel-distributed error with the default variance to the total utility of each product alternative. That error variate is drawn as (using Excel notation) \"=-ln(-ln(Rand()))\".

For HB, you should create \"true\" respondent utilities that are distributed normally. That means you start with one \"true\" population mean vector for your part-worth utilities (again, zero-centered within each attribute). Then, you add normal (zero-centered) deviation to each part-worth for each respondent (just once! held constant across all choice tasks for that respondent), using a normal random draw, with a given variance (perhaps 1.0, if you want to assume heterogeneity of 1.0 across the respondent population). Then, you used those normally perturbed part-worth utilities to score each concept for each respondent. But, prior to projecting each respondent's first choice within each choice task, you need to add Gumbel distributed error as I described previously. Then, have each robotic respondent pick the concept that has the highest total utility (plus error). Within the HB settings, use the prior variance setting equal to prior variance you assumed when building the robotic respondents. This should allow you to recover the true utilities for each respondent (with error) somewhat faithfully, but there could be some \"scale factor\" shift for each respondent that still exists.

Synthetic data set for CBC