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Count Data 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
where P(yi) is the probability of intersection i having yi accidents per year and i is the Poisson parameter for intersection i, which is equal to intersection i’s expected number of accidents per year, E[yi]. Poisson regression models are estimated by specifying the Poisson parameter λi (the expected number of events per period) as a function of explanatory variables. For the intersection accident example, explanatory variables might include intersections’ geometric conditions, signalization, pavement types, visibility, and so on. The most common relationship between explanatory variables and the Poisson parameter is the log-linear model, () λi=EXP(βXi) or, equivalently LN(λi)=βXi,
Mixture Modelling of Discrete Data
Published in Sylvia Frühwirth-Schnatter, Gilles Celeux, Christian P. Robert, Handbook of Mixture Analysis, 2019
As discussed already in Section 9.2.3, zero-inflated Poisson regression models can be regarded as a special case of what has been described above. Being zero, the mean of the inflated part need not to be estimated. The proportion of inflation can be related to some covariates. Dalrymple et al. (2003), for instance, use such a zero-inflated regression model for modelling the number of sudden infant death syndrome cases.
Maritime accidents
Published in Junyi Zhang, Cheng-Min Feng, Routledge Handbook of Transport in Asia, 2018
As the main difference between the negative binomial regression and Poisson model is the assumption on the mean and variance, the Poisson regression can be looked upon as a parameter restriction on the negative binomial regression. Therefore, a Lagrange multiplier test can be computed. For the specification of the test, please refer to Greene (2010, p. 806).
Deep learning-based residual control chart for count data
Published in Quality Engineering, 2022
The Poisson regression is a standard regression model for count response data. The response variable of this model represents the number of events over a period of time such as the number of takeover bids over period of time used in Section 4. Let Yi represent the response (or target) variable and represent a vector of input variables (or features) for Note here that the p input variables can be highly correlated when the number of p is large. The Poisson regression model assumes that the responses Yi’s given independently follow the Poisson distribution. The Poisson distribution has the following probability function:
Analysis of profitability of Pay-As-You-Speed scheme
Published in Traffic Injury Prevention, 2023
Sina Sahebi, Khashayar Khavarian, Habibollah Nassiri
The Poisson regression is a regression to model count or discrete data. The dependent variable in Poisson regression is the probability of a definite section of the road having a specific number of crashes (Anastasopoulos and Mannering 2009). However, it can be used for the number of crashes a person is expected to be responsible for as well (Famoye et al. 2021). The general formulation is presented in Eq. (3). Each section/individual has a unique value which is the expected number of crashes and is assumed to be a function of different variables using an exponential formulation like Eq. (4) (Anastasopoulos and Mannering 2009).
The role of absolute humidity in influenza transmission in Beijing, China: risk assessment and attributable fraction identification
Published in International Journal of Environmental Health Research, 2023
Li Zhang, Chunna Ma, Wei Duan, Jie Yuan, Shuangsheng Wu, Ying Sun, Jiaojiao Zhang, Jue Liu, Quanyi Wang, Min Liu
A distributed lag nonlinear model (DLNM) (Gasparrini et al. 2010) combined with generalized additive models (GAM) was applied to evaluate the association between absolute humidity and Rt of influenza in Beijing. The quasi-poisson regression was used to address overdispersion. The DLNM model structure is stated as following: