قارن الطرق

	النموذج الهرمي البيزي	نموذج منحنى النمو الكامن (LGC)
المجال	بايزي	الإحصاء
العائلة	Bayesian methods	Latent structure
سنة النشأة	2006	1990
صاحب الطريقة	Gelman & Hill (2006); Bayesian multilevel tradition	Meredith & Tisak
النوع	hierarchical probabilistic model	Latent variable / longitudinal growth model
المصدر التأسيسي	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.
الأسماء البديلة	multilevel Bayes, Bayesian multilevel model, Bayesian HLM, partial pooling model	latent growth model, LGC, growth curve model, Gizil Büyüme Eğrisi Modeli
ذات صلة	4	5
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.	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.