方法对比

	分层线性模型 (HLM / 多层模型)	混合效应模型	单因素方差分析	重复测量方差分析
领域	统计学	统计学	统计学	统计学
方法族	Hypothesis test	Regression model	Hypothesis test	Hypothesis test
起源年份	1986	1982	1925	1992
提出者	Raudenbush & Bryk (popularized); Goldstein (parallel development)	Laird & Ware	Ronald A. Fisher	Girden (textbook treatment); Field (2013)
类型	Parametric nested-data regression	Mixed effects regression	Parametric mean comparison	Parametric within-subjects mean comparison
开创性文献	Raudenbush, S.W. & Bryk, A.S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage. ISBN: 978-0761919049	Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38(4), 963–974.	Fisher, R. A. (1925). Statistical Methods for Research Workers. Edinburgh: Oliver and Boyd.	Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed., Ch. 14). SAGE. ISBN: 978-1446249185
别名	HLM, MLM, multilevel modeling, multilevel analysis	LME, LMM, mixed model, random effects model	one-factor ANOVA, single-factor ANOVA, analysis of variance, tek yönlü ANOVA	within-subjects ANOVA, repeated measures analysis of variance, rm-ANOVA, Tekrarlı Ölçüm ANOVA
相关	4	4	4	4
摘要	Hierarchical Linear Modeling (HLM), also known as Multilevel Modeling (MLM), is a parametric statistical method for analyzing nested or clustered data — for example students within classrooms, patients within hospitals, or employees within organizations. Formalized by Raudenbush and Bryk in their 2002 seminal text (building on work from the mid-1980s), HLM simultaneously estimates individual-level and group-level effects while correctly partitioning variance across levels.	A mixed effects model (or linear mixed model) extends ordinary regression by including both fixed effects — population-level parameters shared by all observations — and random effects that capture subject-, group-, or cluster-level variability. It is the standard tool for repeated-measures, longitudinal, and multilevel data where observations within the same unit are correlated.	One-way ANOVA is a parametric hypothesis test that compares the means of three or more independent groups on a single continuous outcome to decide whether at least one group mean differs. It rests on the variance-partitioning framework introduced by Ronald A. Fisher in 1925.	Repeated-measures ANOVA is a parametric hypothesis test that compares three or more measurements taken from the same individuals — typically across time points or conditions — to decide whether their means differ. It extends one-way ANOVA to within-subjects designs, as treated in standard references such as Girden (1992) and Field (2013).