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Risk factors that increased accident severity at US railroad crossings from 2005 to 2015
Published in Gianluca Dell’Acqua, Fred Wegman, Transport Infrastructure and Systems, 2017
In binary logit modeling, the response variable must be dichotomous (e.g., injury accidents vs. no-injury accidents). Ordered logit, and probit, modeling allows for ordinal response variables (e.g., different severity levels of accidents), but it is based on the assumption that the impacts of contributing factors on injury severities are consistent, or proportional, across all observation in all the ordered classes. This assumption may not reflect the heterogeneity nature found in the data being analyzed. Mixed logit models have the flexibility to account for individual heterogeneity of the impacts of different factors on injury severities by allowing parameters to follow a distribution and to randomly vary across observations. However, they may disregard the ordinal nature of the outcome variable.
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.
Analysis of head-on crash injury severity using a partial proportional odds model
Published in Journal of Transportation Safety & Security, 2021
Compared to the results of the partial proportional odds model, the independent variables that adhere to the proportional odds assumption have similarly estimated coefficients with the ordered logit model. For example, the estimation of adverse weather is -0.4977 in the partial proportional odds model and -0.5125 in the ordered logit model. But for the independent variables that violate the proportional odds assumption, the estimated coefficients in the ordered logit model will either overestimate or underestimate the effect of certain variables. For example, the estimated coefficient for speed limit >50 mph is 0.7608 in the ordered logit model. The results in the partial proportional odds model indicate that this coefficient value underestimates the effect of speed limit >50 mph on fatal crash (1.509) and incapacitating injury crash (1.081), and overestimates the effect of the same on non-incapacitating injury crash (0.7128) and possible injury crash (0.6180).
Sustainable transport in neighbourhoods: effect of accessibility on walking and bicycling
Published in Transportmetrica A: Transport Science, 2019
Tayebeh Saghapour, Sara Moridpour, Russel Thompson
OLR models estimate a single equation (regression coefficient) over the levels of the dependent variables. Estimates from the model denote the ordered log-odds (logit) regression coefficients. Interpretation of the ordered logit coefficients is that for a one-unit increase in the predictor, the response variable level is expected to change by its respective regression coefficient in the ordered log-odds scale, while the other variables in the model are held constant. Interpretations of the ordered logit estimates are not dependent on auxiliary parameters. Secondary parameters are used to differentiate the adjacent levels of the response variable. The odds ratio (OR) which is estimated in this model can be obtained by using the exponential function and the coefficient estimate (i.e. eCoef.). To interpret this, persons who are in groups greater than k are compared to those who are in groups less than or equal to k, where k is the number of the response variable levels (Andren et al. 1999). A typical model for the cumulative logits is shown in Equation (5): where, j = 1, … , c−1; c is the total number of categories; x1, x2, … , xn are n explanatory variables; are corresponding coefficients.
Application of partial proportional odds model for analyzing pedestrian crash injury severities in Switzerland
Published in Journal of Transportation Safety & Security, 2019
Lekshmi Sasidharan, Mónica Menéndez
The PPO model estimated for different injury severity levels for all pedestrian–vehicle crashes in Switzerland is given in Table 3. Insignificant parameter estimates are not included in Table 3. The predictors for pedestrian age and speed limit were continuous, and the rest of the predictors are indicator variables. Table 3 shows that the indicators for flat sections, speeding, sight obstructions/restrictions, German speaking areas, wet weather conditions, driver violating pedestrians right of way, national roads, motor cycle, and driving under influence (DUI) all satisfy the proportional odds assumption. Therefore these predictors have same coefficients in all three models. These coefficients can be interpreted in the same way as predictors in ordered logit models. Table 3 shows that the odds for high severity outcome in a pedestrian crash increases by 1.8 times (e0.567) if it occurred on a national road compared to other functional classes of roads. Similarly, speeding increases the odds of higher injury severities in crashes by 40%, holding other predictors constant. The PPO models report that the odds for high severity levels in pedestrian-vehicle crashes is 30% lower for German speaking areas when compared to Italian and French speaking areas in Switzerland.