多層次資料在各個領域中相當普遍，例如鋪面績效資料即是一種極為常見的多層次資料。當利用傳統迴歸方法來分析此種資料時，常會發現違反了對隨機誤差所做的常態分配與固定變異數的假設。因這類型的資料具有層級性，現在通常是採用線性混合效果(LME)模式來分析。線性混合效果模式在資料探索分析、統計模式構建、模式評估與驗證等方面通常會較傳統迴歸分析來得複雜。
本研究將建立一個利用視覺圖技術與線性混合效果模式的系統化分析流程，並以美國AASHO道路試驗的柔性鋪面原始資料來做案例介紹。主要的分析程序包括：探索群組層級與個體層級之成長趨勢、辨識重要參數與不尋常資料、慎選適當的統計模式、選擇一個初始的固定效果模式、選擇具隨機效果的參數和共變異矩陣、建立殘差結構、簡化模式、和模式評估與驗證等。
資料探索分析指出大部份的個體(迴圈/車道)在開始時有較高的現況服務能力指標值(PSI)，但PSI值會隨著時間的增加而降低。在開始時各迴圈/車道PSI值之變動會明顯地較結束時為小。此外，亦可發現個體間之明顯差異。在所構建的初始PSI線性混合效果預測模式中，發現面層厚度、底層厚度、與基層厚度之參數估計值為正，代表當鋪面各層厚度增加時，平均PSI值也會跟著提高。未經季節性調整因子修正過之原始交通荷重次數的參數估計值為負，代表平均PSI值會因原始交通荷重次數增加而降低。結果亦顯示個體的預測值較母體的預測值更接近其觀察值，表示此線性混合效果模式能對資料做較適當的解釋。 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 flexible 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 estimates for AC surface thickness, base thickness, and subbase 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.
