विधियों की तुलना करें

	मजबूत मापन निश्चरता परीक्षण	पुष्टिकारीय कारक विश्लेषण (CFA)	संरचनात्मक समीकरण मॉडलिंग (SEM)
क्षेत्र	मनोमिति	मनोमिति	सांख्यिकी
परिवार	Latent structure	Latent structure	Latent structure
उद्भव वर्ष	1994	1969	1970
प्रवर्तक	Albert Satorra & Peter M. Bentler	Karl Gustav Jöreskog	Karl Jöreskog (LISREL framework, 1970s)
प्रकार	Measurement invariance test with robust corrections	Hypothesis-testing latent variable model	Latent variable / causal modeling
मौलिक स्रोत	Satorra, A. & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent variables analysis: Applications for developmental research (pp. 399–419). Sage.	Jöreskog, K. G. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34(2), 183–202.	Hair, J. F., Black, W. C., Babin, B. J. & Anderson, R. E. (2019). Multivariate Data Analysis (8th ed.). Cengage Learning. ISBN: 978-1473756540
उपनाम	robust MI testing, robust measurement equivalence, non-normal measurement invariance, robust multi-group CFA invariance	CFA, confirmatory FA, measurement model, restricted factor analysis	Yapısal Eşitlik Modellemesi (SEM), structural equation modelling, covariance structure analysis, latent variable modeling
संबंधित	3	4	5
सारांश	Robust measurement invariance testing evaluates whether a psychometric instrument measures the same latent construct in the same way across groups when observed data violate multivariate normality. It adapts standard multi-group CFA sequences by replacing ordinary chi-square statistics with robust alternatives such as the Satorra-Bentler scaled statistic, yielding trustworthy conclusions about factor loadings, intercepts, and residual variances even with skewed or ordinal data.	Confirmatory factor analysis tests a researcher-specified factor structure against observed data. Unlike exploratory approaches, the researcher decides in advance which indicators load on which latent factor, and the model is evaluated by how closely the implied covariance matrix reproduces the sample covariance matrix. CFA is central to scale validation, construct validity assessment, and measurement invariance testing.	Structural equation modeling is a multivariate statistical framework that simultaneously estimates a measurement model — relating observed indicators to latent constructs — and a structural model specifying directional or reciprocal relationships among those constructs. Rooted in the LISREL tradition developed by Karl Jöreskog in the 1970s, SEM is the standard tool for testing complex theoretical models in the social, behavioural, and management sciences.