For over 20 years, the default approach in Sawtooth for constraining part-worth utilities for HB analysis of CBC data (such as levels of price, speed, etc.) has been Simultaneous Tying. Over the years, some researchers have raised concerns regarding speed of estimation and convergence and have turned to using different approaches involving unary (thermometer) coding. And, what about combining unary coding with a newer algorithm (Hamiltonian Monte Carlo) available in the Stan platform? We compare a handful of approaches for utility constraints using a variety of CBC datasets, examining speed, predictive accuracy, quality of the draws, and convergence.
