Analysis of Binary Choice Frequencies With Limit Cases

An extensive evaluation of alternative estimation methods for logistic binary choice probabilities when applied to binary frequency data with limit cases is presented in this paper. The methods examined are: binomial-logistic (BL) model, Berkson's (BK) method, and Haldane's (HL) method. These models are applied to weekly household mode choice data that contained a substantial number of limit cases in which one of the alternatives was never chosen. The results obtained indicate that the BL model is a practical tool that outperforms all the other methods examined in this study. The BL models accommodate limit cases without requiring any additional assumptions or approximations. The BK and HL methods have been shown to offer coefficient estimates similar to, and fits that are somewhat worse than, those obtained by the BL models. These methods remain to be useful tools for the analysis of binary frequency data, especially in initial phases of analysis. In this paper it is also shown that coefficient estimates of HL method are sensitive to the value of the adjustment constant, 6, used to incorporate limit cases and its optimal value may depend on the data at hand.