| This thesis explores extensions of Random Utility Models (RUMs), providing more flexible models and adopting a computational perspective. This includes building new models and understanding their properties such as identifiability and the log concavity of their likelihood functions as well as the development of estimation algorithms.;A special case of RUMs that has received significant attention is the Luce model, for which there are fast inference methods for maximum likelihood estimation. This thesis introduces RUMs including those with exponential family utility distributions, mixture of RUMs, and non-parametric RUMs. Fast inference is achieved through the Monte-Carlo Expectation-Maximization (MC-EM) algorithm. Results on both real-world and simulated data provide support for the ability of these models to better capture heterogeneity in data and for scalable model estimation.;A class of Generalized Method-of-Moments (GMM) algorithms for computing parameters of the Luce model and RUMs is also proposed. The technique is based on breaking full rankings into pairwise comparisons, and then computing parameters that satisfy a set of generalized moment conditions. The conditions for the output of GMM to be unique are identified, leading to a class of pairwise consistent and inconsistent breakings. Theoretical and empirical results show that the algorithms run significantly faster than the classical Minorize-Maximization (MM) and MC-EM approaches, while achieving competitive statistical efficiency.;I propose two preference elicitation scheme for generalized RUMs, in which the utilities can also depend on attributes of agents and alternatives. An empirical study shows that the proposed elicitation scheme increases the precision of estimation for a given number of queries relative to existing approaches.;Furthermore, a model for differentiated items is developed, where I interpret the data as representing preference orders expressed by a population of agents on items, and each agent and item is associated with attributes. I extend the mixture of RUMs method to this setting, with reversible jump MCMC techniques adopted to estimate the parameters of the model and classify agent types. I develop theoretical conditions that establish the uni-modality of the likelihood function and posterior. Empirical results on real and simulated data provide support for improved model fit relative to single type models and for the scalability of the approach. |
