Development of Piecewise Linear Performance Models for Flexible Pavements Using PMS Data
Publication: Journal of Performance of Constructed Facilities
Volume 29, Issue 6
Abstract
This study presents a method to develop piecewise linear (PL) performance models for pavement condition data in a pavement management system (PMS). These condition data are usually ordinal and have more than two severity levels. Ordinal logistic regression is conducted to derive probabilities of each individual severity level. The intersections of probability curves are identified as the breakpoints, which can be used to develop PL models. This proposed method was then applied successfully to develop four PL models, for interstates, U.S. routes, North Carolina routes, and secondary routes, using transverse cracking condition data of flexible pavements in a state DOT’s PMS. Results showed that the PL models reflected actual deterioration trends well and that the proposed method is robust.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors gratefully acknowledge the support and assistant from the Pavement Management Unit (PMU) at the North Carolina Department of Transportation (NCDOT). This research was supported by NCDOT, however, any opinions, findings, and conclusions presented in this paper are those of the authors and do not necessarily reflect the official views of the sponsor.
References
Agresti, A. (1990). Categorical data analysis, 2nd Ed., Wiley, Hoboken, NJ.
AASHTO. (2001). Pavement management guide, Washington, DC.
Armstrong, B. G., and Sloan, M. (1989). “Ordinal regression models for epidemiologic data.” Am. J. Epidemiol., 129(1), 191–204.
Beasley, M. S., Clune, R., and Hermanson, D. R. (2005). “Enterprise risk management: An empirical analysis of factors associated with the extent of implementation.” J. Accounting Publ. Policy, 24(6), 521–531.
Bender, R. (2000). “Calculating ordinal regression models in SAS and S-Plus.” Biometrical J., 42(6), 677–699.
Bender, R., and Grouven, U. (1997). “Ordinal logistic regression in medical research.” J. R. Coll. Physicians London, 31(5), 546–551.
Chen, D., Cavalline, T. L., and Ogunro, V. O. (2014). “Development and validation of pavement deterioration models and analysis weight factors for the NCDOT pavement management system.”, North Carolina Dept. of Transportation.
Corley-Lay, J., Jadoun, F. M., Mastin, J. N., and Kim, Y. R. (2010). “Comparison of flexible pavement distresses monitored by North Carolina department of transportation and long-term pavement performance program.”, Transportation Research Board, Washington, DC, 91–96.
Cragg, J. G., and Uhler, R. S. (1970). “The demand for automobiles.” Can. J. Econ., 3(3), 386–406.
Crane, P. K., et al. (2007). “A comparison of three sets of criteria for determining the presence of differential item functioning using ordinal logistic regression.” Qual. Life Res., 16(1), 69–84.
Dong, Q., Jiang, X., Huang, B., and Richards, S. H. (2013). “Analyzing influence factors to transverse cracking on LTPP resurfaced asphalt pavements through NB and ZINB models.” J. Transp. Eng., 889–895.
Ferri, C., Hernández-Orallo, J., and Salido, M. A. (2003). “Volume under the ROC surface for multi-class problems.” Machine learning: ECML 2003, Springer, Berlin, 108–120.
Hosmer, D. W., Lemeshow, S., and Sturdivant, R. X. (2013). Applied logistic regression, 3rd Ed., Wiley, Hoboken, NJ.
Harrell, F. E. (2001). Regression modeling strategies: With applications to linear models, logistic regression, and survival analysis, Springer, New York.
Langer, W. (2000). The assessment of fit in the class of logistic regression models: A pathway out of the jungle of pseudo R2s, Martin Luther Univ. of Halle Wittenbert, Institute of Sociology, Halle (Saale), Germany.
Lawal, B. (2003). Categorical data analysis with SAS and SPSS applications, Lawrence Erlbaum Associates, Mahwah, NJ.
Li, J. H., Luhr, D. R., and Uhlmeyer, J. S. (2010). “Pavement performance modeling using piecewise approximation.”, Transportation Research Board, Washington, DC, 24–29.
Maddala, G. S. (1983). Limited dependent and qualitative variables in econometrics, Cambridge University Press, New York.
Maple [Computer software]. Waterloo, ON, Maplesoft.
Menard, S. (2000). “Coefficients of determination for multiple logistic regression analysis.” Am. Statistician, 54(1), 17–24.
Menard, S. (2002). Applied logistic regression analysis (No. 106), Sage, Thousand Oaks, CA.
Mittlbock, M., and Schemper, M. (1996). “Explained variation for logistic regression.” Stat. Med., 15(19), 1987–1997.
Mittlbock, M., and Schemper, M. (1999). “Computing measures of explained variation for logistic regression models.” Comput. Methods Programs Biomed., 58(1), 17–24.
North Carolina Deptartment of Transportation (NCDOT) Pavement Management Unit (PMU). (2010). “NCDOT pavement condition survey manual.” 〈https://connect.ncdot.gov/resources/AssetManagement/AssetManagementDocs/2012%20Asphalt%20Pavement%20Survey%20Manual.pdf〉 (Apr. 11, 2012).
Papadimitriou, E., Mylona, V., and Golias, J. (2010). “Perceived level of service, driver, and traffic characteristics: Piecewise linear model.” J. Transp. Eng., 887–894.
Peterson, B., and Harrell, F. E. (1990). “Partial proportional odds models for ordinal response variables.” Appl. Stat., 39(2), 205–217.
Provost, F., and Fawcett, T. (1997). “Analysis and visualization of classifier performance: Comparison under imprecise class and cost distribution.” Proc., Third Int. Conf. on Knowledge Discovery and Data Mining (KDD-97), AAAI Press, Menlo Park, CA, 43–48.
Ryan, S., and Porth, L. (2007). “A tutorial on the piecewise regression approach applied to bedload transport data.”, U.S. Dept. of Agriculture, Forest Service Rocky Mountain Research Station, Fort Collins, CO, 41.
SAS 9.3 [Computer software]. Cary, NC, SAS Institute.
Scott, S. C., Goldberg, M. S., and Mayo, N. E. (1997). “Statistical assessment of ordinal outcomes in comparative studies.” J. Clin. Epidemiol., 50(1), 45–55.
Shahin, M. Y., Kohn, S. D., Lytton, R. L., and McFarland, W. F. (1985). “Pavement M & R budget optimization using the incremental benefit-cost technique.” Proc., North American Pavement Management Conf., Ontario Ministry of Transportation and Communication, Toronto, Canada.
Smith, T. J., and McKenna, C. M. (2012). “An examination of ordinal regression goodness-of-fit indices under varied sample conditions and link functions.” Multiple Linear Regression Viewpoints, 38(1), 1–7.
Swets, J., Dawes, R., and Monahan, J. (2000). “Better decisions through science.” Sci. Am., 283(4), 82–87.
Twarakavi, N. K., and Kaluarachchi, J. J. (2005). “Aquifer vulnerability assessment to heavy metals using ordinal logistic regression.” Ground Water, 43(2), 200–214.
Veall, M. R., and Zimmermann, K. F. (1996). “Pseudo R2 measures for some common limited dependent variable models.” J. Econ. Surv., 10(3), 241–259.
Ysebaert, T., Meire, P., Herman, P. M., and Verbeek, H. (2002). “Macrobenthic species response surfaces along estuarine gradients: Prediction by logistic regression.” Mar. Ecol. Prog. Ser., 225, 79–95.
Information & Authors
Information
Published In
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jan 27, 2014
Accepted: Jun 25, 2014
Published online: Sep 17, 2014
Discussion open until: Feb 17, 2015
Published in print: Dec 1, 2015
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.