We investigate various approaches for imposing ordering constraints on part worths, both in terms of fit on hold-out tasks and run-time for estimating the model. The methods compared are:
• the simultaneous tying method used in Sawtooth CBC/HB, and
• a variant of thermometer coding with one of several transformations to enforce positivity of the deltas.
The transformations investigated include:
• the exponential function;
• the hinge function f(x) = x + |x|, which has a discontinuous derivative at x=0; and
• continuous-derivative approximations to the hinge function.
