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	पुष्टिकारीय कारक विश्लेषण	पदानुक्रमिक रैखिक मॉडलिंग (एचएलएम / बहुस्तरीय मॉडलिंग)	प्रिंसिपल कंपोनेंट एनालिसिस
क्षेत्र	मनोमिति	सांख्यिकी	मशीन अधिगम
परिवार	Latent structure	Hypothesis test	Machine learning
उद्भव वर्ष	1969	1986	2002
प्रवर्तक	Karl Jöreskog	Raudenbush & Bryk (popularized); Goldstein (parallel development)	Jolliffe, I.T. (textbook); Pearson & Hotelling (origins)
प्रकार	Measurement model / latent variable analysis	Parametric nested-data regression	Unsupervised dimensionality reduction
मौलिक स्रोत	Brown, T. A. (2015). Confirmatory Factor Analysis for Applied Research (2nd ed.). Guilford Press. ISBN: 978-1462515363	Raudenbush, S.W. & Bryk, A.S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage. ISBN: 978-0761919049	Jolliffe, I.T. (2002). Principal Component Analysis (2nd ed.). Springer.
उपनाम	Doğrulayıcı Faktör Analizi — Ölçek Doğrulama (CFA), confirmatory factor analysis, measurement model testing	HLM, MLM, multilevel modeling, multilevel analysis	Temel Bileşenler Analizi (PCA), PCA, principal components analysis, Karhunen-Loève transform
संबंधित	6	4	3
सारांश	Confirmatory factor analysis is a measurement modelling technique that tests whether a hypothesised factor structure — typically derived from theory or an earlier exploratory analysis — fits observed data from a new sample. Developed by Karl Jöreskog in 1969, it became the dominant tool for validating psychological scales because it requires the researcher to specify in advance which items belong to which latent factor and then assesses the adequacy of that specification against explicit statistical fit criteria.	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.	Principal Component Analysis (PCA) is an unsupervised dimensionality-reduction method — given its modern textbook treatment by Ian Jolliffe (2002) — that compresses high-dimensional data into fewer dimensions while preserving the maximum possible variance. It re-expresses correlated variables as a small set of uncorrelated principal components ordered by how much of the data's variation each one captures.