قارن الطرق

	نموذج خليط النمو (GMM)	النمذجة الخطية الهرمية (HLM / نمذجة المستويات المتعددة)
المجال	الإحصاء	الإحصاء
العائلة	Latent structure	Hypothesis test
سنة النشأة	1999	1986
صاحب الطريقة	Bengt O. Muthén & Kerby Shedden	Raudenbush & Bryk (popularized); Goldstein (parallel development)
النوع	Latent class / longitudinal growth model	Parametric nested-data regression
المصدر التأسيسي	Muthén, B. O. & Shedden, K. (1999). Finite Mixture Modeling with Mixture Outcomes Using the EM Algorithm. Biometrics, 55(2), 463–469.	Raudenbush, S.W. & Bryk, A.S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage. ISBN: 978-0761919049
الأسماء البديلة	Büyüme Karışım Modeli (Growth Mixture Model — GMM), GMM, latent class growth analysis extension, mixture latent growth curve model	HLM, MLM, multilevel modeling, multilevel analysis
ذات صلة	5	4
الملخص	The Growth Mixture Model, introduced by Muthén and Shedden in 1999, is a longitudinal latent variable method that identifies distinct subpopulations — latent trajectory classes — each following its own growth curve over time. It extends the standard Latent Growth Curve (LGC) model by allowing the sample to be composed of an unknown mixture of classes with different intercepts, slopes, and variance structures.	Hierarchical Linear Modeling (HLM), also known as Multilevel Modeling (MLM), is a parametric statistical method for analyzing nested or clustered data — for example students within classrooms, patients within hospitals, or employees within organizations. Formalized by Raudenbush and Bryk in their 2002 seminal text (building on work from the mid-1980s), HLM simultaneously estimates individual-level and group-level effects while correctly partitioning variance across levels.