Quddus Mohammed A
Transport Studies Group, Department of Civil and Building Engineering, Loughborough University, Epinel Way/Ashby Road, Loughborough, Leicestershire LE11 3TU, United Kingdom.
Accid Anal Prev. 2008 Sep;40(5):1732-41. doi: 10.1016/j.aap.2008.06.011. Epub 2008 Jul 9.
Count data are primarily categorised as cross-sectional, time series, and panel. Over the past decade, Poisson and Negative Binomial (NB) models have been used widely to analyse cross-sectional and time series count data, and random effect and fixed effect Poisson and NB models have been used to analyse panel count data. However, recent literature suggests that although the underlying distributional assumptions of these models are appropriate for cross-sectional count data, they are not capable of taking into account the effect of serial correlation often found in pure time series count data. Real-valued time series models, such as the autoregressive integrated moving average (ARIMA) model, introduced by Box and Jenkins have been used in many applications over the last few decades. However, when modelling non-negative integer-valued data such as traffic accidents at a junction over time, Box and Jenkins models may be inappropriate. This is mainly due to the normality assumption of errors in the ARIMA model. Over the last few years, a new class of time series models known as integer-valued autoregressive (INAR) Poisson models, has been studied by many authors. This class of models is particularly applicable to the analysis of time series count data as these models hold the properties of Poisson regression and able to deal with serial correlation, and therefore offers an alternative to the real-valued time series models. The primary objective of this paper is to introduce the class of INAR models for the time series analysis of traffic accidents in Great Britain. Different types of time series count data are considered: aggregated time series data where both the spatial and temporal units of observation are relatively large (e.g., Great Britain and years) and disaggregated time series data where both the spatial and temporal units are relatively small (e.g., congestion charging zone and months). The performance of the INAR models is compared with the class of Box and Jenkins real-valued models. The results suggest that the performance of these two classes of models is quite similar in terms of coefficient estimates and goodness of fit for the case of aggregated time series traffic accident data. This is because the mean of the counts is high in which case the normal approximations and the ARIMA model may be satisfactory. However, the performance of INAR Poisson models is found to be much better than that of the ARIMA model for the case of the disaggregated time series traffic accident data where the counts is relatively low. The paper ends with a discussion on the limitations of INAR models to deal with the seasonality and unobserved heterogeneity.
计数数据主要分为横截面数据、时间序列数据和面板数据。在过去十年中，泊松模型和负二项式（NB）模型被广泛用于分析横截面和时间序列计数数据，随机效应和固定效应泊松模型以及NB模型则被用于分析面板计数数据。然而，最近的文献表明，尽管这些模型的潜在分布假设适用于横截面计数数据，但它们无法考虑纯时间序列计数数据中经常出现的序列相关性影响。实值时间序列模型，如由博克斯和詹金斯提出的自回归积分移动平均（ARIMA）模型，在过去几十年中已被广泛应用。然而，在对诸如路口交通事故随时间变化的非负整数值数据进行建模时，博克斯和詹金斯模型可能并不适用。这主要是由于ARIMA模型中误差的正态性假设。在过去几年中，一类新的时间序列模型，即整数自回归（INAR）泊松模型，受到了许多作者的研究。这类模型特别适用于时间序列计数数据的分析，因为这些模型具有泊松回归的性质，并且能够处理序列相关性，因此为实值时间序列模型提供了一种替代方案。本文的主要目的是介绍用于英国交通事故时间序列分析的INAR模型类别。考虑了不同类型的时间序列计数数据：观测的空间和时间单位都相对较大的聚合时间序列数据（例如，英国和年份），以及观测的空间和时间单位都相对较小的分解时间序列数据（例如，拥堵收费区和月份）。将INAR模型的性能与博克斯和詹金斯的实值模型类别进行了比较。结果表明，对于聚合时间序列交通事故数据的情况，这两类模型在系数估计和拟合优度方面的性能相当相似。这是因为计数的均值较高，在这种情况下正态近似和ARIMA模型可能是令人满意的。然而，对于分解时间序列交通事故数据中计数相对较低的情况，发现INAR泊松模型的性能比ARIMA模型要好得多。本文最后讨论了INAR模型在处理季节性和未观测到的异质性方面的局限性。
