重複觀測量數之分析：多群體多變項線性成長模式的估計Data Analysis of Repeated Measures: Estimating a Multi-Group Multivariate Linear Growth Model

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