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Transportation facility performance modeling
Published in Zongzhi Li, Transportation Asset Management, 2018
Probabilistic models with limited dependent variables: The Tobit (Tobin's probit or censored regression) model first introduced by James Tobin (1958) is one of the typical cases. The basic idea of the Tobit model is to create a threshold value for the occurrence of an event, such as choosing a facility for maintenance or repair treatment. All facilities are then grouped into two categories: those involving treatments and those without treatments. The joint ML function for the two categories of facilities is formulated to obtain the point estimators. Tobit models are appropriate in cases where the distribution of a dependent variable is censored by a threshold value using a data sample with a mixture of discrete and continuous distributions. Equation 4.5 exhibits the Tobit model Yi*=βXi+ei with Yi={Yi*ifYi*>00,ifYi*≤0 where Yi* = An implicit stochastic index or latent variable observed only when positive from the observations in the datasetYi = The dependent variableXi = The vector of independent variables, X = {X1, X2, … , XK−1}β = The vector of estimated coefficients of independent variables, β = {β0, β1, β2, … , βk−1} with β0 being the estimated constantεi = The random error termi = 1, 2, … , N for the number of observations in the dataset
A conceptualization of the spatial relationship associated with school-related crashes: a case study in Northwest Florida
Published in Transportation Planning and Technology, 2023
Mohammadreza Koloushani, Mahyar Ghorbanzadeh, Eren Erman Ozguven, Alireza Ermagun
We conducted a multivariate Tobit censored regression analysis to evaluate the contribution of correlated crash-related factors concerning the Roadway Network Distance (RND) between the crash location and the nearest school. To define this response variable, we conducted a network analysis in ArcGIS to calculate the RND between crash locations and the nearest school. Concerning the existence of routes detected by the network analysis toolbox, 2,445 crashes (out of 4,778 school-related crashes) have been assigned to their closest school. The RNDs encompass a wide range of values despite not differing significantly for some specific thresholds. For example, school-related crashes that occurred at a distance within a certain threshold from the nearest associated school were classified as considered in a specific category based on their closeness to the school. School-related crashes that occurred farther from the nearest associated school at a predetermined threshold were classified into another specific category with respect to their distance from the school. As such, we needed to utilize a regression model capable of handling non-homogeneous responses. The Tobit censored regression deals with both potential endogeneity and the nonhomogeneity of the response variable. The Tobit censored regression model is developed to estimate the relationship between factors when there is either left-censored (i.e. censored at a low threshold) or right-censored (i.e. censored at a high threshold) dependent variable (Anastasopoulos et al. 2012). According to these descriptions, the crashes that occurred at a distance shorter than 50 ft. from the nearest school were identified and considered with similar characteristics in terms of their closeness to the school. Censoring from the left occurs with the shortest distance value at or below the minimum threshold (50 ft.). In addition, all take on the value of that threshold so that the true value might be equal to the threshold, but it might also be lower. When censoring from the right, values that fall at or above a threshold (1 mile) are censored. Using a left/right-censored limit of 50 ft. and 1 mile, respectively, the multivariate Tobit model with ‘n’ dependent variables is expressed as: where is the dependent variable (the shortest distance between the crash location and the nearest schools), is a vector of independent crash-related variables, is a vector of estimable parameters, and are multivariate normally and independently distributed error terms.