قارن الطرق

	النموذج الهرمي البيزي	الانحدار البايزي	تحليل العوامل التأكيدي (CFA)
المجال	بايزي	بايزي	الإحصاء
العائلة	Bayesian methods	Bayesian methods	Latent structure
سنة النشأة	2006	—	1969
صاحب الطريقة	Gelman & Hill (2006); Bayesian multilevel tradition	—	Karl Jöreskog
النوع	hierarchical probabilistic model	Bayesian linear model	Confirmatory latent variable model
المصدر التأسيسي	Gelman, A. & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955	Brown, T. A. (2015). Confirmatory Factor Analysis for Applied Research (2nd ed.). The Guilford Press. ISBN: 978-1462515363
الأسماء البديلة	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model	bayesian linear regression, probabilistic regression, bayesian regresyon	Doğrulayıcı Faktör Analizi (CFA), confirmatory factor analysis, measurement model
ذات صلة	4	2	4
الملخص	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.	Bayesian regression is a probabilistic version of linear regression that treats the model parameters as uncertain quantities. Instead of returning a single best-fit estimate, it combines prior knowledge with the observed data to produce a full posterior probability distribution for each parameter, from which credible intervals and predictions are read off.	Confirmatory factor analysis tests whether a researcher-specified factor structure fits the observed data. Formalised by Karl Jöreskog in 1969, it is the measurement-model step within structural equation modelling and is the standard tool for validating the factorial structure of scales and questionnaires before comparing groups or estimating latent relationships.