We study choice models with piecewise smooth objective functions and provide conditions under which introducing latent variables derived from regional components yields a censoredmodel– like representation. These latent variables can then be treated as potential outcomes, enabling tractable estimation via the stochastic EM algorithm. We illustrate the framework using two examples: responses to taxes and the (S, s) model. We further estimate a joint retirement decision model for European couples using an interdependent duration framework with our methods. The results provide empirical evidence of complementarities between spouses in the retirement process in Europe.