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利用多層次模式或是階層線性模式進行重複觀測資料的分析，如果個體層次解釋變項包含隨時間變動解釋變項時，在個體層次方程式對它不平減或是總平減所獲得的迴歸係數是一個偏誤的結果，因為這個隨時間變動的解釋變項具有追蹤與橫斷面的資料特性，對個體層次結果變項的影響可以拆解為互斥的組間迴歸係數與組內迴歸係數，因此，必須利用組平減並將組平均數置回截距項方程式方能獲得正確的估計結果。但在不平減、總平減與組平減三種方法下都加上組平均數置回截距項方程式，在隨機截距模型下則會獲得等價的估計結果。本研究整理出這些平減方法之間的統計關係，並利用實徵資料示範分析各種模式，說明之間的差異與等價關係，最後提出研究的結論與建議

組織與管理研究的資料多涉及階層特性，因此多層次模式是當代組織與管理領域的重要研究典範之一，而階層線性模式則是多層次研究主要分析技術。本文針對階層線性模式在多層次研究上有關於技術、測量與方法論所遭遇的問題，進行文獻整理並討論其實務意涵，並依據使用時機、抽樣議題、資料彙總、分析方法、與模式評估與估算等五方面整理出十二項重要議題與解決之道，包括：組內相關係數的意義與判斷準則、多層次研究各層的樣本數問題、變數聚合成組織層次問題、中心化的意義、固定效果與隨機效果的設定、估計法的選擇、適配度的比較、解釋變異量的計算、多元共線性的分析、強韌性標準誤、第一層誤差項變異數與實證貝氏估計值的運用。文中除了進行原理討論之外，並試圖就實務應用的解決方法提出說明。

背景：血液透析病人的疲憊會受疾病本身及治療而有高低的波動，大多數的研究是以過去一週平均疲憊感受，來評估介入措施之成效，然而有研究指出，疲憊可分為透析後疲憊及持續性疲憊，若能先了解有那些不同性質疲憊族群，再測試措施的有效性，也許能更有效降低病人疲憊情況。目的：探討血液透析病人於透析週期八天的疲憊變化型態及其預測因素。方法：採前瞻性觀察法，以方便取樣，收案場所包括新北市三家醫院及一家診所之血液透析室，共有102位個案參與。個案在週期第一天透析時填寫人口學資料、台灣人憂鬱量表、血液透析社會支持量表、特質焦慮量表、匹茲堡睡眠品質量表及疲憊視覺類比量表，並於當日透析結束後開始，每天早、中、晚，連續八天填寫疲憊視覺類比量表；以查閱病歷收集血液生化檢驗值及透析間體重增加情形。結果：研究結果呈現一週期八天的疲憊型態分為疲憊適應組、疲憊急遽變化組及持續疲憊組，以持續疲憊組占最多。當天透析後疲憊程度以疲憊適應組最低，急遽變化組最高；透析後疲憊上升程度（透析後減透析前的疲憊），以急遽變化組上升分數最多，持續疲憊組最低。睡眠品質、特質焦慮及社會支持中的醫護支持為區辨此三組型態的因素。結論：臨床護理人員在透析過程給予個別性的支持、提供改善睡眠品質及緩和焦慮方法來協助病人降低疲憊。

本研究利用「台灣教育長期追蹤資料庫」的一般分析能力與數學分析能力的四波調查結果，配合男、女學生樣本進行多群體多條追蹤資料的線性成長模式估計。在考慮重複觀測資料誤差項在不同時點的變異數非同質與不同時點間的共變數非獨立情況下，以及男、女學生的不同成長軌跡，將誤差項結構設為無限制結構，利用虛擬變項交互項法與虛擬變項多樣本法同時估計不同性別、不同能力的線性成長軌跡變化。由於全部追蹤資料樣本存在遺失值的情形，本研究以階層線性模式（hierarchical linear modeling, HLM）軟體對完整資料2,806位學生進行分析，其估計結果發現，在完整資料的兩條成長軌跡模式中，男、女學生誤差項共變異數矩陣結構相同，但線性成長軌跡不恆等。除此之外，本文並對競爭模式比較的結果在文章最後進行討論並提出相關的建議。

利用多層次模式或是階層線性模式進行重複觀測資料的分析，如果個體層次解釋變項包含隨時間變動解釋變項時，在個體層次方程式對它不平減或是總平減所獲得的迴歸係數是一個偏誤的結果，因為這個隨時間變動的解釋變項具有追蹤與橫斷面的資料特性，對個體層次結果變項的影響可以拆解為互斥的組間迴歸係數與組內迴歸係數，因此，必須利用組平減並將組平均數置回截距項方程式方能獲得正確的估計結果。但在不平減、總平減與組平減三種方法下都加上組平均數置回截距項方程式，在隨機截距模型下則會獲得等價的估計結果。本研究整理出這些平減方法之間的統計關係，並利用實徵資料示範分析各種模式，說明之間的差異與等價關係，最後提出研究的結論與建議。 When analyzing repeated measures by using multilevel modeling (MLM) or hierarchical linear modeling (HLM), if the individual-level independent variables include a time-varying variable and it is modeled as uncentered or grand-mean centered in a level-one equation, then this regression coefficient is a biased estimate. Because repeated measures data comprise longitudinal and cross-sectional parts, the total effect of the time-varying independent variable on the individual outcomes can be decomposed into within- and between-subject regression coefficients. Therefore, the optimal approach is to use group-mean centered in a level-one equation and group means replaced in the intercept equation. In some cases (e.g., the random intercepts model), the three methods, namely uncentered, grand-mean centered, and group-mean centered time-varying variable approaches with group means replacement, are equivalent in MLM and HLM. We adopted a statistical model and empirical data analysis to determine the equivalent relationships and differences among the three centered methods and present a conclusion and recommendations.

本研究利用「台灣教育長期追蹤資料庫」的一般分析能力與數學分析能力的四波調查結果，配合男、女學生樣本進行多群體多條追蹤資料的線性成長模式估計。在考慮重複觀測資料誤差項在不同時點的變異數非同質與不同時點間的共變數非獨立情況下，以及男、女學生的不同成長軌跡，將誤差項結構設為無限制結構，利用虛擬變項交互項法與虛擬變項多樣本法同時估計不同性別、不同能力的線性成長軌跡變化。由於全部追蹤資料樣本存在遺失值的情形，本研究以階層線性模式（hierarchical linear modeling, HLM）軟體對完整資料2,806位學生進行分析，其估計結果發現，在完整資料的兩條成長軌跡模式中，男、女學生誤差項共變異數矩陣結構相同，但線性成長軌跡不恆等。除此之外，本文並對競爭模式比較的結果在文章最後進行討論並提出相關的建議。 This paper demonstrates the data analysis of the repeated measures from the Taiwan Education Panel Survey (TEPS). Based on the four data waves on the TEPS, we consider two abilities (general and mathematic) and two population groups (male and female students) to construct a multi-group multivariate linear growth model. Because the two-group multivariate repeated measures belong to the different populations and the different research variables, the residual terms of linear growth models may imply heterogeneity of the error covariance structure. We treat the error covariance structure as an unrestricted structure to compare the various types of models. The results from the HLM on the complete data (2,806 students) reveal that the male and female students in this study have the same error covariance structure but have distinct linear growth trajectories. In addition, comparisons of the competitive models and related suggestions are discussed in the results and conclusion sections.

The purposes of this study is to probe the impacts of the frequencies of Reading Instruction Activities (RIA) and Reading Strategies Teaching (RST) implemented by teachers, as well as students' Home Education Resources (HER), Reading Attitude (RA), and Self-Assessment (SA) regarding their reading proficiency to students' reading achievement. A two-level database of 128 teachers (macro-level) and matched 3,472 fourth-graders (micro-level) was selected from the Taiwan PIRLS 2006 Database. Multilevel linear modeling (MLM) was then applied to analyze the data. The results indicated that in micro-level, HER, RA, and SA can significantly explain students' reading achievement in a positive way. In the macro-level, neither RIA nor RST showed a significant contextual effect on students' reading achievement. Additionally, the specific interaction among the cross-level analysis was likely to involve the frequencies of RIA, enhancing the relationship between students' RA and their reading achievement. Based on the resear

本研究旨在探究教師閱讀教學行為（閱讀教學活動和閱讀策略教學頻率）與學生閱讀態度、閱讀能力自我評價對於學生閱讀成就的影響。研究資料為臺灣地區「促進國際閱讀素養研究」（PIRLS 2006），研究者挑選128 名教師和相配對的3,472位學生，以多層次線性模式進行分析。結果顯示，個體層次的學童家庭教育資源、閱讀態度、閱讀能力自我評價對於閱讀成就皆具有顯著的正向影響。其次，總體層次的教師閱讀教學活動頻率和閱讀策略教學頻率對於學童閱讀成就則沒有顯著的脈絡效果。第三，跨層次交互作用可能具有特定性，教師閱讀活動教學頻率可能對於學生閱讀態度產生強化作用。最後，本文提出對於閱讀教育的省思和資料庫分析研究的建議。 The purposes of this study is to probe the impacts of the frequencies of Reading Instruction Activities (RIA) and Reading Strategies Teaching (RST) implemented by teachers, as well as students’ Home Education Resources (HER), Reading Attitude (RA), and Self-Assessment (SA) regarding their reading proficiency to students’ reading achievement. A two-level database of 128 teachers (macro-level) and matched 3,472 fourth-graders (micro-level) was selected from the Taiwan PIRLS 2006 Database. Multilevel linear modeling (MLM) was then applied to analyze the data. The results indicated that in micro-level, HER, RA, and SA can significantly explain students’ reading achievement in a positive way. In the macro-level, neither RIA nor RST showed a significant contextual effect on students’ reading achievement. Additionally, the specific interaction among the cross-level analysis was likely to involve the frequencies of RIA, enhancing the relationship between students’ RA and their reading achievement. Based on the research findings, the researcher also addresses issues pertaining to the limitations of the study and suggestions for future research.

Multilevel study is one of the important contemporary research paradigms in organizational and management field, due to the fact that the data collected in organizational and management research frequently involve nested structure. Hierarchical linear modeling is the most frequently used technique for analyzing multilevel data. In this paper, the twelve key issues in multilevel research and/or using HLM software were reviewed, and provided their exact meanings and feasible solutions. The 12 key issues included intraclass correlation coefficient, sample sizes, formation of organizational constructs, centering problems, fixed effect and random effect, estimation methods, goodness of fit index, explained variation, multicollinearity, robust standard error, level one variance equation, and empirical Bayes estimates. In addition to the discussions on principles of the issues, implications and solutions to research practices were illustrated in the present paper.