Methoden vergleichen

	Bayes'sche Mischungsmodellierung	Latente Klassenanalyse (LCA)
Fachgebiet	Statistik	Statistik
Familie	Latent structure	Latent structure
Entstehungsjahr	1997 (Richardson & Green Bayesian formulation)	1950s–1968
Urheber	Richardson & Green (seminal Bayesian treatment, 1997); broader Bayesian mixture roots trace to Dempster, Laird & Rubin (EM, 1977) and Titterington, Smith & Makov (1985)	Paul F. Lazarsfeld
Typ	Latent-class / model-based clustering	Latent variable / person-centered classification
Wegweisende Quelle	Fruhwirth-Schnatter, S., Celeux, G. & Robert, C. P. (Eds.) (2019). Handbook of Mixture Analysis. CRC Press / Chapman & Hall. ISBN: 9780367733995	Goodman, L. A. (1974). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61(2), 215–231.
Aliasnamen	Bayesian mixture model, BMM, Bayesian model-based clustering, Bayesian finite mixture	LCA, latent class model, latent categorical analysis, finite mixture of multinomials
Verwandt	4	6
Zusammenfassung	Bayesian mixture modeling represents the population as a weighted sum of K component distributions and estimates all unknowns — mixing weights, component parameters, and even the number of components — through posterior inference. It extends classical mixture analysis by placing priors on every parameter and quantifying uncertainty over latent group assignments rather than treating them as fixed.	Latent class analysis identifies unobserved subgroups — latent classes — within a population by finding patterns of responses across a set of categorical observed indicators. It is the categorical-variable counterpart of cluster analysis, but grounded in an explicit probabilistic model, and is widely used in social, health, and behavioral sciences to discover typologies in survey or diagnostic data.