Poisson Regression Models of Infrastructure Transition Probabilities
Publication: Journal of Transportation Engineering
Volume 121, Issue 3
Abstract
Markovian transition probabilities have been used extensively in the field of infrastructure management, to provide forecasts of facility conditions. However, existing approaches used to estimate these transition probabilities from inspection data are mostly ad hoc and suffer from several statistical limitations. In this paper, econometric methods for the estimation of infrastructure deterioration models and associated transition probabilities from inspection data are presented. The first method is based on the Poisson regression model and follows directly from the Markovian behavior of infrastructure deterioration. The negative binomial regression, a generalization of the Poisson model that relaxes the assumption of equality of mean and variance, is also presented. An empirical case study, using a bridge inspection data set from Indiana, demonstrates the capabilities of the two methods.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ben-Akiva, M., Ceder, A., Cheng, L., and Liss, M. (1988). “Estimation of intersection traffic safety improvements.”Final Rep., Prepared for Massachusetts Department of Public Works, Ctr. for Transp. Studies, MIT, Cambridge, Mass.
2.
Ben-Akiva, M., and Lerman, S. R. (1985). Discrete choice analysis: theory and application to travel demand. The MIT Press, Cambridge, Mass.
3.
Ben-Akiva, M., and Ramaswamy, R.(1993). “An approach for predicting latent infrastructure facility deterioration.”Transp. Sci., 27(2), 174–193.
4.
Busa, G. D. (1985). “Modelling concrete bridge deck deterioration,” MSc thesis, Massachusetts Institute of Technology, Cambridge, Mass.
5.
Butt, A. A., Feighan, K. J., Shahin, M. Y., and Carpenter, S. (1987). “Pavement performance prediction model using the Markov process.”Transp. Res. Record 1123, Transp. Res. Board, National Research Council, Washington, D.C.
6.
Cameron, A. C., and Trivedi, P. K.(1986). “Econometric models based on count data: comparisons and applications of some estimators and tests.”J. Appl. Econometrics, 1, 29–53.
7.
Cameron, A. C., and Trivedi, P. K.(1990). “Regression-based tests for overdispersion in the Poisson model.”J.Econometrics, 46, 347–364.
8.
Carnahan, J. V., Davis, W. J., and Shahin, M. Y.(1987). “Optimal maintenance decisions for pavement management.”J. Transp. Engrg., ASCE, 113(5), 554–572.
9.
Dean, C., and Lawless, J. F.(1989). “Tests for detecting overdispersion in Poisson regression models.”J. Am. Statistical Assoc., 84(406), 467–472.
10.
Federal Highways Administration (FHWA). (1979). “Recording and coding guide for structure inventory and appraisal of the nation's bridges.”Rep., U.S. Department of Transportation, Washington, D.C.
11.
Feighan K. J., Shahin, M. Y., Sinha, K. C., and White T. D. (1988). “Application of dynamic programming and other mathematical techniques to pavement management systems.”Transp. Res. Record 1200, Transp. Res. Board, National Research Council, Washington, D.C., 90–98.
12.
Frome, E. L., Kutner, M. H., and Beauchamp, J. J.(1973). “Regression analysis of Poisson-distributed data.”J. Am. Statistical Assoc., 68(344), 935–940.
13.
Gourieroux, A., Monfort, A., and Trognon, A.(1984). “Pseudo maximum likelihood methods: applications to Poisson models.”Econometrica, 52(3), 701–720.
14.
Greene, W. H. (1990). Econometric analysis, MacMillan Publishing Co., New York, N.Y.
15.
Greene, W. H. (1991). “LIMDEP version 6.0.”User's manual and reference guide. Econometric Software, Inc., Bellport, N.Y.
16.
Hatcher, S. G., and Mahmassani, H. S. (1992). “Daily variability of route and trip scheduling decisions for the evening commute.”Transp. Res. Record 1357, Transp. Res. Board, National Research Council, Washington, D.C.
17.
Hauer, E., and Persaud, B. (1990). “How to estimate the safety of rail-highway grade crossings and the safety effect of warning devices.”Transp. Res. Record 1114, Transp. Res. Board, National Research Council, Washington, D.C., 131–140.
18.
Hausman, J., Hall, B., and Griliches, Z.(1984). “Econometric models for count data with an application to the patents—R & D relationship.”Econometrica, 52(4), 909–938.
19.
Jiang, Y., Saito, M., and Sinha, K. C. (1988). “Bridge performance prediction model using the Markov Chain.”Transp. Res. Record 1180, Transp. Res. Board, Washington, D.C., 25–32.
20.
Lerman, S. R., and Gonzales, S. L.(1980). “Poisson regression analysis under alternate sampling strategies.”Transp. Sci., 14(4), 346–364.
21.
Madanat, S.(1993). “Optimal infrastructure management decisions under uncertainty.”Transp. Res. C, 1(1), 77–88.
22.
Madanat, S., and Ben-Akiva, M.(1994). “Optimal inspection and repair policies for infrastructure facilities.”Transp. Sci., 28(1), 55–62.
23.
Mannering, F. (1989). “Poisson analysis of commuter flexibility in changing route and departure times.”Transp. Res., 23B(1), 53–60.
24.
McCullagh, P., and Nelder, J. A. (1983). Generalized linear models . Chapman and Hall, London, England.
25.
McKelvey, R. D., and Zavoina, W.(1975). “A statistical model for the analysis of ordinal level dependent variables.”J. Math. Sociology, 4(2), 103–120.
26.
Ross, S. M. (1989). “Introduction to probability models.” 4th Ed., Academic Press, Inc., New York, N.Y.
27.
Shahin, M., and Kohn, S. (1981). “Pavement maintenance management for roads and parking lots.”Tech. Rep. M-294, Constr. Engrg. Res. Lab., U.S. Army Corps of Engineers, Champaign, Ill.
28.
Shahin, M. Y., Nunez, M. M., Broten, M. R., Carpenter, S. H., and Sameh, A. (1987). “New techniques for modelling pavement deterioration.”Transp. Res. Record 1123, Transp. Res. Board, National Research Council, Washington, D.C.
29.
Sinha, K. C., Fwa, T. F., Sharaf, E. A., Tee, A. B., and Michael, H. L. (1984). “Indiana highway cost allocation study.”Final Rep. FHWA/IN/JHRP-84-20, Purdue University, West Lafayette, Ind.
Information & Authors
Information
Published In
Journal of Transportation Engineering
Volume 121 • Issue 3 • May 1995
Pages: 267 - 272
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: May 1, 1995
Published in print: May 1995
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.