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Linear Regression
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
Censored dependent variables are analyzed using a number of techniques, the most popular of which is the tobit model as introduced by James Tobin (1958). The tobit model takes the form () Yi*=βXi+εi,i=1,2,…,N,Yi=Yi*ifYi*>0=0ifYi*≤0,
Maritime accidents
Published in Junyi Zhang, Cheng-Min Feng, Routledge Handbook of Transport in Asia, 2018
The Tobit model is designed to deal with situations where the dependent variable is censored—certain kinds of observations are not observable. For example, if using a linear model to explain the oil spill size, we can only observe the positive spill size; the negative part is censored. If we want to model the number of ship accidents using a set of explanatory variables, we can only observe the positive number of accidents. In this case, a latent variable y* is assumed to bridge the gap between the observed dependent variable Y and the explanatory variable X, i.e., y*=X′β+ɛ
Analysis in Two Stages: Techniques for Joint Assessment with DEA
Published in Fabio Sartori Piran, Daniel Pacheco Lacerda, Luis Felipe Riehs Camargo, Analysis and Management of Productivity and Efficiency in Production Systems for Goods and Services, 2020
Fabio Sartori Piran, Daniel Pacheco Lacerda, Luis Felipe Riehs Camargo
Unlike simple and multiple linear regressions, the Tobit regression was developed with the objective of predicting models with limited dependent variables. The basis of the Tobit model is similar to linear regression, but it assumes a truncated or censored normal distribution, and becomes an effective method to estimate the relationship between a truncated or censored dependent variable and other independent variables (Amemiya, 1984).
Bootstrap-Tobit model for maritime accident economic loss considering underreporting issues
Published in Transportmetrica A: Transport Science, 2021
Guorong Li, Jinxian Weng, Shanshan Fu
Table 3 tabulates the Bootstrap-Tobit model coefficients for the supplemented maritime accident data. According to Table 3, the coefficients of the collision, sinking, fire/explosion, and capsizing are positive, suggesting that these accident types are associated with higher economic loss while contact and grounding accidents are associated with lower economic loss. In this case study, the marginal effect is calculated to represent the extent of how much the economic loss changes. The marginal effects in a Tobit model could be calculated based on the exponent of the estimated coefficient, which translates to a percent change in economic loss resulting from one unit change in the variables. With the calculated marginal effects for each Tobit model, the marginal effects for the Bootstrap-Tobit model could be determined with the same computing process of Bootstrap-Tobit model coefficients (i.e. Eqs. (12)-(14)). Figure 9 presents the marginal effects of economic loss contributory factors according to the results of both models including the Tobit model and the Bootstrap-Tobit model considering the underreporting issue.
Differences between telecommuters and commuters: the case of the Twin Cities metropolitan area
Published in Transportation Planning and Technology, 2021
This study employs Tobit models to highlight the differences in travel time and distance between telecommuters and commuters. The Tobit model has been widely adopted in transportation literature to explore travel behavior (c.f., Anastasopoulos, Tarko, and Mannering 2008; Chatman 2003; Cirillo, Liu, and Tremblay 2017; Heres-Del-Valle and Niemeier 2011; Khan, Kockelman, and Xiong 2014). The Tobit model refers to a class of regression models in which the observed range of the dependent variable is censored in some way, such as with zero-inflated data (Hayashi 2000). Some respondents in this study reported no travel time and distance, and thus they have a zero value for travel outcome. The Tobit model is presented when the dependent variable has many numbers of zero values because of the corner solution. The basic Tobit model expresses the observable variable yt given xt, as follows:
Irrigators’ willingness to pay for the adoption of soil moisture monitoring tools in South-Eastern Africa
Published in International Journal of Water Resources Development, 2020
Fentahun Abebe, Alec Zuo, Sarah Ann Wheeler, Henning Bjornlund, Andre van Rooyen, Jamie Pittock, Makarius Mdemu, Mario Chilundo
Given the nature of our survey data, a Tobit model was chosen as the best method to estimate the determinants of farmers’ WTP for the sensor array and for weekly access to the reader. Zero-WTP responses are common in CV studies, and the Tobit model is one of the regression methods most suitable for analyzing data with censored responses (Tobin, 1958). The unique feature of the Tobit model is that it attempts to incorporate each piece of information (censoring values as well as values greater than censoring point) into the investigation (Tobin, 1958). In our survey, there are farmers with WTP responses clustered at 0 (bottom limit) for both sensor array and reader, and WTP values of USD75 and USD50 as an upper censoring response for sensor array and reader, respectively, so the Tobit method was appropriate.