手法を比較

	ベイズ混合効果モデル	階層線形モデル（HLM）
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	1990s–2000s (modern Bayesian MCMC era)	1992
提唱者	Gelman, Hill, and the broader Bayesian hierarchical modeling tradition	Bryk & Raudenbush
種類	Bayesian regression model	Multilevel linear regression
原典	Gelman, A., & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. ISBN: 978-0521686891	Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage Publications. ISBN: 978-0761919049
別名	Bayesian multilevel model, Bayesian random effects model, Bayesian LME, Bayesian hierarchical mixed model	HLM, multilevel linear model, nested data model, random coefficient model
関連	5	4
概要	The Bayesian mixed effects model extends the classical mixed effects framework by placing prior distributions on all parameters — fixed effects, random effect variances, and residual variance — and updating them with data to produce full posterior distributions. This provides coherent uncertainty quantification for both population-level and group-level effects simultaneously.	The Hierarchical Linear Model (HLM) is a multilevel regression method designed for data in which lower-level units (e.g., students, patients) are nested within higher-level groups (e.g., schools, hospitals). It simultaneously models within-group relationships and between-group variation, producing unbiased estimates and correct standard errors that ordinary regression cannot provide for nested data.