مقایسهٔ روش‌ها

	مدل‌سازی معادلات ساختاری بیزی (BSEM)	مدل سلسله مراتبی بیزی	مدل منحنی رشد پنهان (LGC)
حوزه	بیزی	بیزی	آمار
خانواده	Bayesian methods	Bayesian methods	Latent structure
سال پیدایش	2012	2006	1990
پدیدآور	Bengt Muthén & Tihomir Asparouhov	Gelman & Hill (2006); Bayesian multilevel tradition	Meredith & Tisak
نوع	Bayesian latent variable model	hierarchical probabilistic model	Latent variable / longitudinal growth model
منبع بنیادین	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.	Meredith, W. & Tisak, J. (1990). Latent Curve Analysis. Psychometrika, 55(1), 107–122.
نام‌های دیگر	BSEM, Bayesian latent variable model, approximate zero constraints SEM, Bayesçi Yapısal Eşitlik Modeli	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model	latent growth model, LGC, growth curve model, Gizil Büyüme Eğrisi Modeli
مرتبط	6	4	5
خلاصه	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.	The latent growth curve model is a structural equation modelling approach introduced by Meredith and Tisak (1990) for analysing change over time. It treats each individual's starting point (intercept) and rate of change (slope) as latent variables, simultaneously estimating the average trajectory across the sample and the extent to which individuals differ in their own trajectories.