手法を比較

	ベイズ階層モデル	階層線形モデル（HLM）
分野	ベイズ	統計学
系統	Bayesian methods	Regression model
提唱年	2006	1992
提唱者	Gelman & Hill (2006); Bayesian multilevel tradition	Bryk & Raudenbush
種類	hierarchical probabilistic model	Multilevel linear regression
原典	Gelman, A. & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.	Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage Publications. ISBN: 978-0761919049
別名	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model	HLM, multilevel linear model, nested data model, random coefficient model
関連	4	4
概要	Bayesian hierarchical modelling, popularised by Gelman and Hill (2006), is a Bayesian approach to nested data structures — such as students within schools within districts — that estimates separate parameters at each level while allowing those levels to share statistical strength through a mechanism called partial pooling. Where a classical hierarchical linear model treats group means as fixed unknown quantities, the Bayesian version places hyperprior distributions on those group means so that information flows freely across levels, producing more reliable group-level estimates whenever any individual group has few observations.	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.