Accounting for Censoring and Unobserved Heterogeneity in Pavement Cracking

Abstract

Most fatigue cracking models in use have been developed using the ordinary least squares (OLS) method. However, fatigue cracking data (or any type of cracking data) consists of censored data since it has a lower limit of zero. This can cause bias in the fatigue cracking model because the data is not continuous but has positive probability mass at zero. Additionally, when data is selected only from pavements that exhibit cracking, bias will result because the estimates are based on a nonrandom sample. Moreover, bias can also be generated by unobserved factors not included in the fatigue cracking model. This type of bias can be removed by considering the deterioration history of each pavement section, if the unobserved factors are section-specific. Based on a long-term pavement performance (LTPP) dataset consisting of SPS-1 pavement sections, the authors have modeled fatigue cracking of pavement structures. The data were initially used in modeling fatigue cracking by means of OLS and by a corner solution regression model (Tobit) that accounts for data censoring in fatigue cracking. The Tobit model was used, analyzing the data as pooled and also as a panel dataset (by random-effects), to check for possible bias in the model due to unobserved heterogeneity. The OLS fatigue cracking model exhibits several types of biases due to heterogeneity and erroneous assumptions in the modeling process. The model estimates and test statistics used to evaluate them indicated that the preferred fatigue cracking model was the random effects Tobit model because it accounts for the censoring and heterogeneity bias. Estimating the model by accounting for these types of bias in the data resulted in significant changes in the effects of different parameters affecting fatigue through time.