| Summary: | 碩士 === 淡江大學 === 土木工程學系碩士班 === 99 === Multilevel data are very common in many fields. Pavement performance data is a very common example of multilevel data. While analyzing this type of data using conventional regression techniques, the normality assumptions with random errors and constant variance were often violated. Because of its hierarchical data structure, multilevel data are often analyzed using Linear Mixed-Effects (LME) models. The exploratory analysis, statistical modeling, and the examination of model-fit of LME models are more complicated than those of standard multiple regressions.
A systematic modeling approach using visual-graphical techniques and LME models was proposed and demonstrated using the original AASHO road test rigid pavement data. The proposed approach including exploring the growth patterns at both group and individual levels, identifying the important predictors and unusual subjects, choosing suitable statistical models, selecting a preliminary mean structure, selecting a random structure, selecting a residual covariance structure, model reduction, and the examination of the model fit was further discussed.
Exploratory analysis of the data indicated that most subjects (loop/lane) have higher mean PSIs at the beginning of the observation period, and they tend to decrease over time. The spread among the subjects is substantially smaller at the beginning than that at the end. In addition, there exist noticeable variations among subjects. A preliminary LME model for PSI prediction was developed. The positive parameter estimate for slab thickness indicates that higher mean PSI values tend to occur on thicker pavements. The parameter estimate of unweighted applications is negative indicating that lower PSI values for higher load applications. The prediction line of the within-group predictions follows the observed values more closely than that of the population predictions indicating the proposed LME model provides better explanation to the data.
Furthermore, nonlinear regression technique was also adopted in an attempt to develop modified rigid pavement design equations for single- and tandem- axle loads separately. The derived equivalent axle load factors (EALF) or load equivalency factors (LEF) using different design equations were compared to the existing LEFs. Even though reasonable results have been obtained, the newly derived LEFs representing quite a departure from the well-known fourth-power rule should be cautioned and further investigated.
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