So sánh phương pháp

	Mô hình Rasch đa cấp	Multilevel Measurement Invariance
Lĩnh vực	Trắc lượng tâm lý	Trắc lượng tâm lý
Họ	Latent structure	Latent structure
Năm ra đời	1997	2000s
Người khởi xướng	Adams, Wilson & Wu	Muthén, Asparouhov, and colleagues
Loại	Hierarchical item response model	Measurement model evaluation
Công trình gốc	Adams, R. J., Wilson, M. & Wu, M. (1997). Multilevel item response models: An approach to errors in variables regression. Journal of Educational and Behavioral Statistics, 22(1), 47–76.	Muthén, B. O., & Asparouhov, T. (2009). Multilevel factor analysis of class and student achievement components. Journal of Educational and Behavioral Statistics, 34(2), 250–270.
Tên gọi khác	hierarchical Rasch model, random-effects Rasch model, multilevel IRT Rasch, MRCML model	MLMI, multilevel factorial invariance, cross-level measurement invariance, multilevel CFA invariance
Liên quan	5	3
Tóm tắt	The multilevel Rasch model extends the standard Rasch model to data with a nested structure — for example, students within classrooms within schools — by embedding person ability parameters inside a hierarchical linear model. It yields item difficulty estimates on a logit scale while simultaneously partitioning person-ability variance across cluster levels and correcting standard errors for non-independence.	Multilevel measurement invariance testing evaluates whether a latent construct is measured equivalently both within clusters (e.g., individuals within teams) and between clusters (e.g., team-level aggregates). It extends standard measurement invariance procedures to nested data structures commonly encountered in organisational, educational, and cross-cultural research.