Using Generalized Linear Mixed Models to Predict the Number of Roadway Accidents: A Case Study in Hamilton County, Tennessee

Eric M. Laflamme1, *, Peter Way2, Jeremiah Roland2, Mina Sartipi2
1 Department of Mathematics, Plymouth State University, Plymouth, NH 03264, England
2 College of Engineering and Computer Science, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA

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© 2020 Laflamme et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: ( This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Mathematics, Plymouth State University, Plymouth, NH 03264, United States;
Tel: 603-724-5336; E-mail:



A method for identifying significant predictors of roadway accident counts has been presented. This process is applied to real-world accident data collected from roadways in Hamilton County, TN.


In preprocessing, an aggregation procedure based on segmenting roadways into fixed lengths has been introduced, and then accident counts within each segment have been observed according to predefined weather conditions. Based on the physical roadway characteristics associated with each individual accident record, a collection of roadway features is assigned to each segment. A mixed-effects Negative Binomial regression form is assumed to approximate the relationship between accident counts and several explanatory variables including roadway characteristics, weather conditions, and several interactions between them. Standard diagnostics and a validation procedure show that our model form is properly specified and suitably fits the data.


Interpreting interaction terms leads to the follow findings: 1) rural roads with cloudy conditions are associated with relative increases in accident frequency; 2) lower/moderate AADT and rainy weather are associated with relative decreases in accident frequency, while high AADT and rain are associated with relative increases in accident frequency; 3) higher AADT and wider pavements are associated with relative increases in accident frequency; and 4) higher speed limits in residential areas are associated with relative increases in accident frequency.


Results illustrate the complicated relationship between accident frequency and both roadway features and weather. Therefore, it is not sufficient to observe the effects of weather and roadway features independently as these variables interact with one another.

Keywords: Accident frequency model, Generalized linear mixed model, Negative binomial regression, Roadway features, Weather, Railways.