Bayesian Hierarchical Poisson Regression Models: An Application to a Driving Study With Kinematic Events

REFERENCES

• Albert , P. S. , Follmann , D. A. , Wang , S. A. and Suh , E. B. 2002 . “A Latent Autoregressive Model for Longitudinal Binary Data Subject to Informative Missingness,” . Biometrics , 58 : 631 – 642 .
   PubMed Web of Science ®Google Scholar
• Balakrishnan , S. and Madigan , D. 2006 . “A One-Pass Sequential Monte Carlo Method for Bayesian Analysis of Massive Datasets,” . Bayesian Analysis , 1 : 345 – 362 .
   Web of Science ®Google Scholar
• Botts , C. H. and Daniels , M. J. 2008 . “A Flexible Approach to Bayesian Multiple Curve Fitting,” . Computational Statistics and Data Analysis , 52 : 5100 – 5120 .
   PubMed Web of Science ®Google Scholar
• Chen , M.-H. and Ibrahim , J. G. 2000 . “Bayesian Predictive Inference for Time Series Count Data,” . Biometrics , 56 : 678 – 685 .
   PubMed Web of Science ®Google Scholar
• Cowles , C. and Carlin , B. P. 1996 . “Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review,” . Journal of the American Statistical Association , 91 : 883 – 904 .
   Web of Science ®Google Scholar
• Diggle , P. J. , Liang , K. Y. and Zeger , S. L. 1994 . Analysis of Longitudinal Data , London : Clarendon Press .
   Google Scholar
• DiMatteo , I. , Genovese , C. R. and Kass , R. E. 2001 . “Bayesian Curve Fitting With Free Knot Splines,” . Biometrika , 88 : 1055 – 1071 .
   Web of Science ®Google Scholar
• Gilks , W. R. and Wild , P. 1992 . “Adaptive Rejection Sampling for Gibbs Sampling,” . Applied Statistics , 41 : 337 – 348 .
   Web of Science ®Google Scholar
• Green , P. J. 1995 . “Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination,” . Biometrika , 82 : 711 – 732 .
   Web of Science ®Google Scholar
• Guo , F. , Klaver , S. G. , Hankey , J. M. and Dingus , T. A. 2010 . “Near Crashes as Crash Surrogate for Naturalistic Driving Studies,” . Journal of the Transportation Research Board , 2147 : 66 – 74 .
   Web of Science ®Google Scholar
• Harvey , A. C. 1989 . Forecasting, Structural Time Series Models and the Kalman Filter , Cambridge : Cambridge University Press .
   Google Scholar
• Hastings , W. K. 1970 . “Monte Carlo Sampling Methods Using Markov Chains and Their Applications,” . Biometrika , 57 : 97 – 109 .
   Web of Science ®Google Scholar
• Hay , J. L. and Pettitt , A. 2001 . “Bayesian Analysis of Time Series of Counts,” . Biostatistics , 2 : 433 – 444 .
   PubMedGoogle Scholar
• Huang , L. , Chen , M.-H. and Ibrahim , J. G. 2005 . “Bayesian Analysis for Generalized Linear Models With Nonignorably Missing Covariates,” . Biometrics , 61 : 767 – 780 .
   PubMed Web of Science ®Google Scholar
• Ibrahim , J. G. , Chen , M.-H. and Ryan , L. M. 2000 . “Bayesian Variable Selection for Time Series Count Data,” . Statistica Sinica , 10 : 971 – 987 .
   Web of Science ®Google Scholar
• Karim , M. R. and Zeger , S. L. 1992 . “Generalized Linear Models With Random Effects-Salamander Mating Revisited,” . Biometrics , 48 : 631 – 644 .
   PubMed Web of Science ®Google Scholar
• Klauer , S. G. , Dingus , T. A. , Neale , V. L. , Sudweeks , J. D. and Ramsey , D. J. 2006 . The Impact of Driver Inattention on Near Crash/Crash Risk: An Analysis Using the 100-Car Naturalistic Driving Study Data , Washington, , DC : National Highway Traffic Safety Administration .
   Google Scholar
• Liu , J. S. 1994 . “The Collapsed Gibbs Sampler in Bayesian Computations With Applications to a Gene Regulation Problem,” . Journal of the American Statistical Association , 89 : 958 – 966 .
   Web of Science ®Google Scholar
• Liu , J. S. and Sabatti , C. 2000 . “Generalised Gibbs Sampler and Multigrid Monte Carlo for Bayesian Computation,” . Biometrika , 87 : 353 – 369 .
   Web of Science ®Google Scholar
• McCulloch , C. E. , Searle , S. R. and Neuhaus , J. M. 2008 . Generalized, Linear, and Mixed Models (2nd ed.) , New York : Wiley .
   Google Scholar
• Simons-Morton , B. G. , Ouimet , M. C. , Zhang , Z. , Klauer , S. E. , Lee , S. E. , Wang , J. , Albert , P. S. and Dingus , T. A. 2011a . “Crash and Risky Driving Involvement Among Novice Adolescent Drivers and Their Parents,” . American Journal of Public Health , 101 : 2362 – 2367 .
   PubMed Web of Science ®Google Scholar
• Simons-Morton , B. G. , Ouimet , M. C. , Zhang , Z. , Klauer , S. E. , Lee , S. E. , Wang , J. , Albert , P. S. and Dingus , T. A. 2011b . “The Effect of Passengers and Risk-Taking Friends on Risky Driving and Crashes/Near Crashes Among Novice Teenagers,” . Journal of Adolescent Health , 49 : 587 – 593 .
   PubMed Web of Science ®Google Scholar
• Simons-Morton , B. G. , Zhang , Z. , Jackson , J. C. and Albert , P. S. 2012 . “Do Elevated Gravitational-Force Events While Driving Predict Crashes and Near Crashes?,” . American Journal of Epidemiology , 15 : 1075 – 1079 .
   Web of Science ®Google Scholar
• Smith , J. Q. 1979 . “A Generalization of the Bayesian Forecasting Model,” . Journal of Royal Statistical Society, Series B , 41 : 375 – 387 .
   Google Scholar
• Spiegelhalter , D. J. , Best , N. G. , Carlin , B. P. and van der Linde , A. 2002 . “Bayesian Measures of Model Complexity and Fit” (with discussion), . Journal of Royal Statistical Society, Series B , 64 : 583 – 639 .
   Google Scholar
• Wahlberg , A. E. 2007 . “Aggregation of Driver Acceleration Behavior Data: Effects on Stability and Accident Prediction,” . Safety Science , 45 : 487 – 500 .
   Web of Science ®Google Scholar
• Zeger , S. L. 1988 . “A Regression Model for Time Series of Counts,” . Biometrika , 75 : 621 – 629 .
   Web of Science ®Google Scholar
• Zhang , Z. , Albert , P. S. and Simons-Morton , B. G. 2012 . “Marginal Analysis of Longitudinal Count Data in Long Sequences: Methods and Applications to a Driving Study,” . The Annals of Applied Statistics , 6 : 27 – 54 .
   PubMed Web of Science ®Google Scholar