Threshold Negative Binomial Autoregressive Model for Overdispersed Road Traffic Crash Fatalities Counts with Structural Breaks

Abstract

Road traffic crashes (RTCs) continue to represent one of the most severe public health challenges
in Nigeria, causing high levels of fatalities and injuries each year. Modeling RTC counts is difficult
because the data typically exhibits overdispersion, nonlinear dependence, and structural breaks
arising from interventions, enforcement, or policy changes. This study sets out to develop a
Threshold Negative Binomial Autoregressive model with Structural Breaks (NB-TAR-SB) inorder
to address the challenges of overdispersion, nonlinear dependence, and structural breaks. The study
extends the work of Liu et al., (2019) and Yang et al. (2018) adapting negative binomial
innovations for overdispersed counts, a threshold mechanism for nonlinear regime switching, and
break adjustments through Bai-Perron multiple breakpoint tests. Parameters are estimated using
conditional maximum likelihood, and thresholds and breakpoints are chosen by minimizing profile
likelihood and BIC. The model's theoretical properties depend on nonlinear stationarity and
ergodicity conditions, which guarantee that the estimators are consistent and asymptotically
normal. Diagnostics including the Box-Pierce test, mean squared error (MSE), and root mean
squared error (RMSE) were used to validate model adequacy. Nigeria Annual RTC fatality data
from 1993 to 2024 was used. The preliminary analysis revealed the presence of overdispersion,
while structural break detection revealed policy-driven shifts, particularly in the early 2000s. The

NB-TAR-SB outperformed benchmark models; it achieved a residual independence of 0.826 (Box-
Pierce pvalue), with the lowest forecast errors of (MSE = 0.968, RMSE = 0.984). These results

demonstrate that incorporating both threshold dynamics and structural breaks yields a more
flexible and powerful tool for modeling RTCs. The proposed NB-TAR-SB model thus offers a
novel methodological and applied framework for evaluating interventions and informing effective
road safety policy in Nigeria.
Keyword: Nonlinear Count Time Series, Threshold Autoregressive model, Structural Breaks,
Conditional Maximum Likelihood, Road Traffic Fatalities.