The problem of modeling choice behavior has received considerable attention. The simplest choice situation is a paired comparison experiment in which items are compared two at a time. The Thurstone-Mosteller and Bradley-Terry models are the most commonly used models for such experiments. Underlying both these models are the assumptions that the choice probabilities associated with a comparison are the same for all judges and that all comparisons are performed independently of one another. Two models, that are based on the Bradley-Terry model approach, are introduced in which these assumptions are relaxed. For both of these models, methods of parameter estimation and hypothesis testing are presented. The method of pseudo-maximum likelihood estimation is discussed and extended to the case of product multinomial distribution. Also, a Wald statistic is derived that performs tests of hypotheses using the pseudo-MLEs. The various parameter estimation and hypothesis testing techniques for four different paired comparison models are applied in two examples. Listings of the computer programs that performed the calculations for the models are given in appendices. Finally, the models are compared to one another and discussed in terms of their ease of application and relative influence on the sensitivity of goodness of fit tests.