U. S. Department of Transportation
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- Extensions to the Multinomial Logit Model
- Future Research
- Appendix C:Summary of Modeling Results
ConclusionBoth Bayesian and frequentist schools of thought have their merits. Frequentist methods result in point estimates of parameters and are easily implemented. However, frequentist methods do not allow the researcher to include any information that is not in the data, and may suffer from poor performance on small samples. Bayesian methods result in a distribution of a parameter, have improved small sample properties, and allow for the inclusion of additional information. Bayesian methods offer theoretical improvements; however, without strong priors, these theoretical improvements are mitigated. Implementation is a major concern for Bayesian methods, likely requiring a significant resource investment to get the estimation working properly.
The multinomial probit has been suggested as an alternative to the multinomial logit specification, primarily to avoid the unfavorable IIA property. However, due to the computational concerns regarding the multinomial probit, other alternatives have been developed. The two major developments have been nested logit models and random parameter models. Nested models are one way to address the IIA property of multinomial logits. Nested models achieve this by grouping the choices into several subsets with similar unobserved differences.119 Thus, unobserved differences are similar across groups but not between groups. This avoids the unwanted IIA property introduced into the multinomial logit framework. It is important to note that the nesting is merely a statistical artifact and does not imply any sort of decision tree.120 The interpretation of a decision tree is a behavioral one imposed by the researcher, but is not reflected in the underlying statistics. Nested logit models are useful in studying mode choice as it can account for similar unobserved effects between choices (such as between busses and trains).121 A nesting approach may be useful for modeling runway incursion severity if the different categories have significantly different unobserved effects. For example, a nesting structure with two branches, one with C and D while the other contained A and B, may be applicable. Another alternative that attempts to relax the IIA assumption of the multinomial logit is the random parameters model.122 Essentially, this model allows the parameters of the top-level model to vary in a systematic way. That is, a model of mode choice could estimate a coefficient for mode price. That coefficient could then be allowed to vary in a systematic way with education, income, and other variables. This allows the model to be extremely flexible in terms of the correlation structure of the random disturbance terms. However, this model can be difficult to implement. For a more complete discussion, see Greene.123 Baht and Gossen provides an example of an implementation of this model.124
Appendix C:Summary of Modeling ResultsThe following table summarizes the results presented in the body of the paper. Rows represent different variables while the different columns represent the variety of tests and models detailed in the report. The general direction of the effect is given. If the estimated relationship had a p-value less than 0.10, it is reported as an X in the table, indicating it was included in the model or a test was performed, but it is deemed insignificant. Empty cells represent that no test was run or that the variable was not included in the model. Positive indicates that increasing values of the variable (or in the case of binary variables, being coded as a yes) increase the severity of an incursion. Negative indicates that opposite – increasing values decrease the severity of the incursion.
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