本文旨在介紹階層線性模式（hierarchical linear model，簡稱HLM）的發展、基本理論，並藉由實例的分析及結果的解釋來說明HLM的應用。文中首先概要說HLM目前的發展、介紹各領域中所使用的名稱，以目前發展成熟的電腦統計軟體等。其次，以二階層HLM為例，說明HLM的基本原理，介紹完整模式（以階層－方程式的截距及斜率做為階層二方程式之結果變項的迴歸（intercepts-and shopes-as-outcomes），並就一般常用的五種次模式（submodel）分別說明其基本假設、特色及使用時機。所提出之次模式計有隨機效果單因子變異數分析（one-way ANOVA with random effects）、以階層一方程式中的各組平均數做為階層二方式之結果變項的迴歸模式（means-as-outcomes regression）、隨機效果單因子共變數分析（one-way ANCOVE with random effects）、隨機係數的迴歸模式（random coefficients regression model）、帶有非隨機變化之斜率的模式（a model with nonrandomly varying slopes）等五種模式。最後，本文以陳素琴、蘇育任和林原宏（民84）就中部地區國小五、六年級學生所進行之「影響自然科成績相關因素研究」為實例進行統計分析及結果解釋，並對今後有關研究提出建議。

The purpose of this paper was to introduce the theory of “Hierarchical Linear Model” (HLM). The authors also gave a analysis of real data. By this way, the reader will realize the application of HLM. First, in this paper, we introduced the different names of HLM in other research area. Besides this, the software of HLM was be introduced. Second, we explain the theory of HLM. In addition to the “full model”, of HLM, we also raised five submodels of HLM, which were “one-way ANOVA with random effects”, “means-as-outcomes regression”, “one-way ANCOVA with random effects”, “random coefficients regression model”, and “a model with nonrandomly varying slopes”. In this paper, the assumption, characteristics, and application of the above five submodels were be discussed. Finally, we analyzed the data, which was from the plan of NSC, and explained the results. From the analysis we gave some suggestions for further research.