• Model fit assessment evolved from central chi-square tests to practical fit indices and invariance testing, shaping guidelines for SEM evaluation. Foundational GOF critiques [10], the development of Comparative Fit Indices [4], factorial invariance approaches [11], procedures for testing measurement invariance [15], and broad SEM testing frameworks [3].

• Latent variable modeling emphasizes measurement structures and the consequences of measurement error, developing robustness to nonnormal data and latent variates. Core works include Structural Equations with Latent Variables [1], robustness of normal-theory methods [19], theoretical improvements in Mean and Covariance Structure Analysis [9], latent-variable SEM for experiments [20], and practical covariance-structure issues [5].

• SEM as a general framework for theory testing and application across psychology, education, and management. Foundational conceptions and applications are presented in Structural Equation Modeling: Concepts, Issues, and Applications (1996) [2], 1997 counterpart [6], covariance-structure applications in education/psychology [14], and critical perspectives on SEM practices [16].

• Design and estimation challenges in SEM include sample size effects, model misspecification, and estimation under nonnormality, guiding robust practices. Key studies examine how sample size, estimation method, and misspecification affect fit [7], design choices in two-level data [18], formal evaluation/modification via interval estimation [17], and methodology critiques [16].