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Ordered Probability Models
Published in Simon Washington, Matthew Karlaftis, Fred Mannering, Panagiotis Anastasopoulos, Statistical and Econometric Methods for Transportation Data Analysis, 2020
Simon Washington, Matthew Karlaftis, Fred Mannering, Panagiotis Anastasopoulos
Maximizing this log-likelihood function is subject to the constraint 0 ≤ μ1 ≤ μ2 … ≤ μI–1. If the assumption is made that ε in Equation (14.1) is logistically distributed across observations with mean = 0 and variance = 1, an ordered logit model results and the derivation proceeds the same as for the ordered probit model. Because the ordered probit model is not afflicted with the estimation difficulties encountered in estimating the multinomial probit model for unordered discrete data, the ordered probit is usually chosen over the ordered logit because of the underlying assumption of normality.
Investigation of the causes of runway excursions
Published in Gianluca Dell’Acqua, Fred Wegman, Transport Infrastructure and Systems, 2017
Table 5 presents the parameters of the ordered probit model that has been developed for the estimation of the probabilities of the causes that generate the runway excursions. Coefficient estimates are provided for this model, along with standard errors, as well as confidence intervals for each variable. The modelling results allowed to infer interesting considerations, both general and in relation to individual types of accidents.
How have ride-sourcing users adapted to the first wave of the COVID-19 pandemic? evidence from a survey-based study of the Greater Toronto Area
Published in Transportation Letters, 2021
Patrick Loa, Sanjana Hossain, Yicong Liu, Khandker Nurul Habib
An ordered probit model was developed to investigate the factors influencing ride-sourcing frequency during the COVID-19 pandemic among ride-sourcing users. The ordered response framework was used (as opposed to the count regression framework) because ride-sourcing frequency was presented as a categorical value in the SiSTM survey. In the ordered probit model, the outcome is determined based on the value of a latent variable, which is modeled as a function of explanatory variables. As shown in Equation 1, the latent variable is converted into a discrete outcome by applying a censoring mechanism, which is defined based on the values of the threshold parameters. The formulation of the ordered probit model is listed below (Greene and Hensher 2003):
Empirical analysis of level of service at toll plaza by using ordered probit model
Published in Transportation Letters, 2020
Yogeshwar V. Navandar, Mahaveer Singh, Ashish Dhamaniya, D. A. Patel
The IS rating analysis is used to quantify the most influencing variables which should be improved for achieving a better level of service, while the Order Probit models are required to identify the effect of various attributes on the users’ perceived LOS at the toll plaza. The ordered probit is basically the generalized case of probit analysis where more than two outcomes of the ordinal dependent variable exist. In such situations, the dependent variable holds the values within the range of poor to excellent. However, many software packages are available for constructing an ordered probit model. In this study NLOGIT 5.0 (2007) software package is used to develop the order probit model. The LOS rating from ‘A’-‘F’ scale is converted into ordinal data. Ordinal data corresponding to LOS ‘A’ is zero and that for LOS ‘F’ is 5. The results obtained through the application of the ordered probit model are presented in Table 5. The developed model is tested at a 5 % significance level. According to Table 5, a positive sign of coefficient indicates that an increase in the variable gives a higher probability that a worse level of service (LOS ‘F’) will be perceived by users. Similarly, a negative sign of coefficient means, an increase in the variable quality or quantity will result in a higher probability of a better level of service (LOS A) perceived by users.
The effect of information on changing opinions toward autonomous vehicle adoption: An exploratory analysis
Published in International Journal of Sustainable Transportation, 2020
Parvathy Vinod Sheela, Fred Mannering
Finally, the possibility of unobserved heterogeneity in the data was accounted for by allowing parameters to vary across respondents. A standard random parameters approach was used with (please see Mannering, Shankar, & Bhat, 2016, for a full description of alternate heterogeneity modeling approaches), where βkn is the parameter estimate for explanatory variable k (one of the elements in the parameter vector β) for respondent n, βk is the mean parameter estimate for explanatory variable k, and φn is a randomly distributed term (e.g., normally distributed term with mean zero and variance σ2). Estimation of the random parameters ordered probit was undertaken by simulated maximum likelihood approaches (Washington et al., 2011). Previous studies have shown that Halton draws provide a more efficient distribution of simulation draws than purely random draws (Bhat, 2003). In the forthcoming model estimations 1,000 Halton draws were used in the simulated likelihood functions, a number that has been shown to be more than sufficient to provide accurate parameter estimates (Anastasopoulos & Mannering, 2009; Bhat, 2003; Halton, 1960).