Conjoint choice experiments are widely used to study consumer preference among a set of product alternatives. Traditional models (such as the multinomial logit model) for conjoint choice analysis imply some unrealistic consumer behaviors which are often not observed in real conjoint choice data. Additionally, they are at lack of connection with underlying psychological decision process. In this dissertation, a stochastic model, the Poisson race model, is studied and applied to the context of conjoint choice analysis. It assumes that decision making is a process of accumulating information in favor of each alternative. When the information accumulated reaches certain threshold, a choice is made. The accumulation of information for each alternative follows a Poisson process and is independent of those of other alternatives.
A set of theoretical results are derived for the Poisson race model, including expressions for choice probabilities, monotonicity, effect of thresholds and the behavior implications. The behavior implications includes results on whether the family of Poisson race models has the properties of Independence of Irrelevant Alternatives (IIA) and transitivity and under what conditions such properties fall apart. Theoretically, the Poisson race model not only captures the traditional multinomial logit model as a special case, but also describes a much broader range of decision making behavior.
A new class of Poisson race model is proposed to model dependence in conjoint choice data. It incorporates a dependence structure which captures the relationship between the attributes of the choice alternatives and which appropriately moderates the randomness inherent in the race. The proposed dependent model assumes that there is a shared process tracking the information shared by the alternatives in a choice set. The formulae to calculate the choice probabilities are derived and the tie-breaking mechanism are discussed. The new model is also extended to the conjoint choice data with more than two alternatives in a choice set. The new model is applied to real conjoint choice data on consumer preference of credit cards with binary and trinary choice sets and is shown to have markedly superior performance to independent Poisson race models and to the multinomial logit model.