مقایسهٔ روش‌ها

	مدل سلسله مراتبی بیزی	تحلیل عاملی تأییدی (CFA)	مدل منحنی رشد پنهان (LGC)
حوزه	بیزی	آمار	آمار
خانواده	Bayesian methods	Latent structure	Latent structure
سال پیدایش	2006	1969	1990
پدیدآور	Gelman & Hill (2006); Bayesian multilevel tradition	Karl Jöreskog	Meredith & Tisak
نوع	hierarchical probabilistic model	Confirmatory latent variable model	Latent variable / longitudinal growth model
منبع بنیادین	Gelman, A. & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.	Brown, T. A. (2015). Confirmatory Factor Analysis for Applied Research (2nd ed.). The Guilford Press. ISBN: 978-1462515363	Meredith, W. & Tisak, J. (1990). Latent Curve Analysis. Psychometrika, 55(1), 107–122.
نام‌های دیگر	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model	Doğrulayıcı Faktör Analizi (CFA), confirmatory factor analysis, measurement model	latent growth model, LGC, growth curve model, Gizil Büyüme Eğrisi Modeli
مرتبط	4	4	5
خلاصه	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.	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.	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.