This work on gap acceptance is based on the premise that the decision to accept/reject a gap happens in a person's mind and therefore must be based on the perceived gap and not the measured gap. The critical gap must also exist in a person's mind and hence, together with the perceived gap, is a latent variable. Finally, it is also proposed that the critical gap is influenced by various exogenous variables such as subject and opposing vehicle types, and perceived waiting time. Mathematical models that (i) incorporate systematic and random distortions during the perception process and (ii) account for the effect of the various influencing variables are developed. The parameters of these models are estimated for two different gap acceptance data sets using the maximum likelihood technique. The data is collected as part of this study. The estimated parameters throw valuable insights into how these influencing variables affect the critical gap. The results corroborate the initial predictions on the nature of influence these variables must exert and give strength to the gap acceptance decision-making construct proposed here. This work also proposes a methodology to estimate a measurable/observable world emulator of the latent variable critical gap. The use of the emulator critical gap provides improved estimates of derived quantities like the average waiting time of subject vehicles. Finally, studies are also conducted to show that the number of rejected gaps can work as a reasonable surrogate for the influencing variable, waiting time.