قارن الطرق

	نمذجة المعادلات الهيكلية البايزية (BSEM)	النموذج الهرمي البيزي	الانحدار البايزي
المجال	بايزي	بايزي	بايزي
العائلة	Bayesian methods	Bayesian methods	Bayesian methods
سنة النشأة	2012	2006	—
صاحب الطريقة	Bengt Muthén & Tihomir Asparouhov	Gelman & Hill (2006); Bayesian multilevel tradition	—
النوع	Bayesian latent variable model	hierarchical probabilistic model	Bayesian linear model
المصدر التأسيسي	Muthén, B. & Asparouhov, T. (2012). Bayesian SEM: A More Flexible Representation of Substantive Theory. Psychological Methods, 17(3), 313–335.	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
الأسماء البديلة	BSEM, Bayesian latent variable model, approximate zero constraints SEM, Bayesçi Yapısal Eşitlik Modeli	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model	bayesian linear regression, probabilistic regression, bayesian regresyon
ذات صلة	6	4	2
الملخص	Bayesian SEM, introduced by Muthén and Asparouhov in 2012, extends classical structural equation modeling by placing prior distributions on factor loadings, path coefficients, and covariances. Instead of returning a single maximum-likelihood estimate, it uses Markov chain Monte Carlo to produce a full posterior distribution for every parameter, enabling principled uncertainty quantification in models with latent variables.	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.